#euclid division algorithm class 10

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CBSE Solutions For Class 10 Mathematics Chapter 1 Real Numbers

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NCERT Class 10

Chapter: Real Numbers

Exercise 1.1

Question 3: An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?

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#RealNumbers #Class10Maths

In this lecture I have discussed the Meaning & Method to find HCF / GCD and Euclid's Division Algorithm of Chapter 1 Real Numbers Class 10 Maths.  

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NCERT Solutions for Class 10 Maths

NCERT Solutions for Class 10 maths covers all exercise questions given in the CBSE textbook. You can download this as free pdf from this page. Our best Mathematics master teachers have reviewed all the class 10 maths ncert solutions of exercise questions that will help you solve all the NCERT class 10 maths questions without any problem. We at Learncbse provide free PDF solutions for NCERT maths class 10 for your ease. You can also share the link of our Learncbse website with your classmates so that they can also download CBSE class 10th math NCERT solution. At any point of time, if you have any doubt while going through the class 10 maths NCERT solutions, The online classes will be conducted by one of our best mathematics teachers. You can even talk to the tutor as you would in a normal tuition class. 

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NCERT Solutions for Class 10 Maths - Free PDF Download Class 10 being a whole new experience for you as it will be the very first time when you will be appearing for the board exams. Speaking of which, a thorough knowledge of all the chapters along with NCERT Solutions for Class 10 Maths can really help you to understand the subject better in less time. Below given are the chapters and the topics and exercises entailed in each of them. Scroll down to get well-versed with each and every chapter of CBSE Class 10 Maths.

Chapter 1 – Real Numbers

NCERT Class 10 Math Chapter 1, Real Numbers, is the extension of the topics learnt in 9th class. Sections 1.2 and 1.3 of this chapter contains some very important properties of positive integers, namely Euclid’s division algorithm and the Fundamental Theorem of Arithmetic. Furthermore, you will be revisiting Irrational Numbers in section 1.4 whereas Revisiting Rational Numbers and Their Decimal Expansions will be included in Section 1.5. Euclid’s division algorithm has a lot to do with divisibility of integers. It has plethora of applications associated with the divisibility properties of integers. NCERT Class 10 Maths Chapter 1, Real Numbers will be highly beneficial to compute the HCF of two positive integers.

Chapter 2 - Polynomials

Polynomials has total of four exercises however the last exercise is optional. In the first exercise, you need to find zeroes of polynomials p(x). In the second exercise, there are two questions. You have to verify the relationship between the zeroes and the coefficients in the first, while in the second, you have to find a quadratic polynomial. The third exercise has a total of five questions in which you have to do division of polynomials and obtain zeroes of polynomials. Then comes the optional exercise which has five questions in which you need to find zeroes of polynomials.

Chapter 3 - Pair of Linear Equations in Two Variables

There is an introduction part in the beginning of this chapter explaining the concepts of Linear equations in two Variables. You will learn some further complex topics while revising concepts that you have learned in class 9. This chapter has a total of seven exercises in which the last exercise is optional again. You will see three world problems given in the first exercise. In the second exercise, there are a total of seven questions. The third exercise has three questions. The fourth exercise has two questions. The fifth exercise has a total of` five questions in which you have to solve the pair of linear equations through various methods given. The sixth exercise has two questions. The last exercise is optional. Some important topics covered in this chapter are graphical representations, Pair of Linear Equations in Two Variables, Algebraic Methods of Solving a Pair of Linear Equations, Graphical Method of Solution of a Pair of Linear Equations, Elimination Method, Substitution Method, Cross-Multiplication Method and Equations Reducible to a Pair of Linear Equations in Two Variables.

Chapter 4 - Quadratic Equations

You will study quadratic equations and number of ways to find their roots. You will also get to learn some applications of quadratic equations in our daily life situations. There is a total of four exercises in this chapter. The first exercise has two questions, in the first you will need to find check whether equations are quadratic equations or not while in the second you have to convert world problem into quadratic equations. You need to find the roots of quadratic equations by factorisation in the second exercise. You will be finding the roots of quadratic equations in the third exercise also. The fourth exercise has five questions based on finding the roots. Solution of a Quadratic Equation by Completing the Square, Solution of a Quadratic Equation by Factorisation, and Nature of Roots are the main topics studied in this chapter.

Chapter 5 - Arithmetic Progressions

Arithmetic Progressions, chapter 5 of Class 10 Maths, deals with an introduction to Arithmetic Progression with the help of simple daily life examples and gradually deals with the topics entailed and their complexities. Four exercises are given in this chapter divided into various questions in which we have to find the term. Overall, you will learn how to find the nth terms and the sum of n consecutive terms, and in turn use the acquired knowledge in solving some daily life problems.

Chapter 6 - Triangles

There are six exercises in chapter 6, Triangles, including one optional having different set of questions based on the properties of triangles. This chapter has a total of 9 theorems and is very important for all the students of class 10 Maths for their class 10 Board exam.

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Chapter 7 - Coordinate Geometry

A total of four exercises are given in the chapter. The questions are based on finding the distance between the two points whose coordinates are provided and area of a triangle formed by three given points.

Chapter 8 - Introduction to Trigonometry

This chapter has a total of four exercises comprising of various questions mainly on finding trigonometric ratios of the sides of a right triangle with respect to the acute angles of that triangle, called trigonometric ratios. Trigonometric Ratios, Trigonometric Ratios of Specific Angles, Trigonometric Identities and Trigonometric Ratios of Complementary Angles are the main topics you will learn in this chapter.

Chapter 9 - Some Applications of Trigonometry

In this chapter, you will be studying about some very interesting ways in which trigonometry is uded in the daily life around you. This chapter has only one exercise and the questions of which are based on the practical applications of trigonometry.

Chapter 10 - Circles

Circles has just two exercises. The first exercise contains basic questions, while the second has various questions in which you have to prove the given equations.

Chapter 11 - Constructions

In this chapter, there are two exercise where you have to draw various constructions such as division of line segments, construction of Tangents to a Circle and the questions are based on them.

Chapter 12 - Areas related to Circles

There are three exercises that cover all the questions of the area of a circle and finding the areas of two special ‘parts’ of a circular region.

Chapter 13 - Surface Areas and Volumes

In this chapter, there are five exercises and all of them will deal with the problems of finding areas and volumes of different solids such as cube, cuboid and cylinder.

Chapter 14 - Statistics

You will see a total of four exercises in this chapter. The questions will be based on finding mean, median and mode from ungrouped data to that of grouped data. You will also be solving questions related to cumulative frequency, how to draw cumulative frequency curves and the cumulative frequency distribution topics.

Chapter 15 - Probability

Out of the two exercise in this chapter, one is optional. The questions are based on finding the probability of getting a situation mostly on coins and dice.

Why Learncbse.in

Learncbse.in NCERT Solutions for Class 10 Maths enables you to understand all the basic & advance level concepts after solving each & every exercise question. Our Maths teachers especially focus on clearing out your concepts and providing you with a thorough understanding of all the topics. You are taught on a one-to-one basis by our most dedicated teachers. We at Learncbse.in don't believe in just recorded lectures as they don't prove helpful in solving doubts related to any of the book solutions.

To assess your progress on a regular basis, you are tested by our maths tutors at a definite interval of time. The results are shared with your parents to keep them on the same page as well. Another benefit of Learncbse.in is that you get to choose the pace of the learning of the lesson and the timing of the live tutoring session. The lesson plan is customized according to your requirements. The live sessions are also recorded and are available free of cost to all the students and their parents later for review and revision purposes. Another biggest advantage of studying with Learncbse.in is that you can choose to study class 10 maths ncert solutions either on your PC or through your Android mobile devices after downloading our Instant doubt solving app! You can either join us as a regular student or contact us whenever you have doubts and want to prepare for your tests or examinations! We want our NCERT solutions for class 10 maths to prove highly beneficial for you!

There are several ways with which you can avail the benefits of our NCERT Class 10 Maths Solutions. Let’s see what they are after a brief description. Stepping into Class 10 is the best experience of your life as you will be experimenting and facing new things which might appear very exciting to you. As mentioned already that it will be the first time in your life when you will be appearing for the class 10 board exams. Maths is counted among the most dreadful subjects which is feared by a lot of the students. This is the reason why along with NCERT Solutions for class 10 Maths, we have provided the detailed chapter-wise content so that you face no problem while solving the tricky questions of class 10 Maths. Students are advised to keep the Maths NCERT Solutions class 10 handy so that they can prepare short notes that are highly beneficial for class 10 Maths exam. You can include important formulas and theorems and make short notes of it. Chapters like Coordinate Geometry and Constructions need undivided attention which can be gained by solving NCERT Solutions for class 10 Maths and going through the root cause of each and every problem you are facing problem with. We wish you all the best for your journey along with the preparation of Class 10 Maths and good fortune to all your endeavours.

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Class 10 Maths NCERT Solutions Chapter 1 Real Numbers

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers Class 10 Maths Real Numbers Exercise 1.1

Question 1 Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Solution: (i) 135 and 225

Method 1:

Method 2:

(ii) 196 and 38220 Method 1:

Method 2:

(iii) 867 and 255 Method 1:

Method 2:

Question 2: Show that any positive odd integer is of the form 6q…

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Class 10 Maths NCERT Solutions Chapter 1 Real Numbers

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers Class 10 Maths Real Numbers Exercise 1.1

Question 1 Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Solution: (i) 135 and 225

Method 1:

Method 2:

(ii) 196 and 38220 Method 1:

Method 2:

(iii) 867 and 255 Method 1:

Method 2:

Question 2: Show that any positive odd integer is of the form 6q…

[learncbse6]

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers Class 10 Maths Real Numbers Exercise 1.1

Question 1 Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Solution: (i) 135 and 225

Method 1:

Method 2:

(ii) 196 and 38220 Method 1:

Method 2:

(iii) 867 and 255 Method 1:

Method 2:

Question 2: Show that any positive odd integer is of the form 6q…

[ncertsolutionsbooks]

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers

Class 10 Maths NCERT Solutions Chapter 1 Real Numbers Class 10 Maths Real Numbers Exercise 1.1

Question 1 Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Solution: (i) 135 and 225

Method 1:

Method 2:

(ii) 196 and 38220 Method 1:

Method 2:

(iii) 867 and 255 Method 1:

Method 2:

Question 2: Show that any positive odd integer is of the form 6q…

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NCERT Solutions for Class 10 Maths PDF Download

NCERT Solutions for Class 10 Maths for all the activities from Chapters 1 to 15 are given here. These solutions are curated by our master personnel to help understudies in their board test arrangements. Understudies searching for the NCERT Solutions for Class 10 Maths can download all part shrewd pdf to locate a superior way to deal with take care of the issues. 

The responses to the inquiries present in the NCERT books are without a doubt the best examination material an understudy can get hold of. These CBSE NCERT Solutions of Class 10 Maths will likewise assist understudies with building a more profound comprehension of ideas canvassed in Class 10 Maths course reading. Rehearsing the course reading addresses will assist understudies with examining their degree of readiness and the information on ideas. The solutions to these inquiries present in the books can assist understudies with clearing their questions rapidly.

NCERT Solutions for Class 10 Maths Chapters and Exercises NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers In Chapter 1 of Class 10, students will explore real numbers and irrational numbers. The chapter starts with the Euclid’s Division Lemma which states that “Given positive integers a and b, there exist unique integers q and r satisfying a = bq + r, 0=r<b”. The Euclid’s Division algorithm is based on this lemma and is used to calculate the HCF of two positive integers. Then, the Fundamental Theorem of Arithmetic is defined which is used to find the LCM and HCF of two positive integers. After that, the concept of an irrational number, a rational number and decimal expansion of rational numbers are explained with the help of theorem.

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials In Polynomials, the chapter begins with the definition of degree of the polynomial, linear polynomial, quadratic polynomial and cubic polynomial. This chapter has a total of 4 exercises including an optional exercise. Exercise 2.1 includes the questions on finding the number of zeroes through a graph. It requires the understanding of Geometrical Meaning of the Zeroes of a Polynomial. Exercise 2.2 is based on the Relationship between Zeroes and Coefficients of a Polynomial where students have to find the zeros of a quadratic polynomial and in some of the questions they have to find the quadratic polynomial. In Exercise 2.3, the concept of division algorithm is defined and students will find the questions related to it. The optional exercise, 2.4 consists of the questions from all the concepts of Chapter 2.

NCERT Solutions for Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables This chapter explains the concept of Pair of Linear Equations in Two Variables. This chapter has a total of 7 exercises, and in these exercises, different methods of solving the pair of linear equations are described. Exercise 3.1 describes how to represent a situation algebraically and graphically. Exercise 3.2 explains the methods of solving the pair of the linear equation through Graphical Method. Exercises 3.3, 3.4, 3.5 and 3.6 describe the Algebraic Method, Elimination Method, Cross-Multiplication Method, Substitution Method, respectively. Exercise 3.7 is an optional exercise which contains all types of questions. Students must practise these exercises to master the method of solving the linear equations.

NCERT Solutions for Class 10 Maths Chapter 4 Quadratic Equations In this chapter, students will get to know the standard form of writing a quadratic equation. The chapter goes on to explain the method of solving the quadratic equation through the factorization method and completing the square method. The chapter ends with the topic on finding the nature of roots which states that, a quadratic equation ax² + bx + c = 0 has

Two distinct real roots, if b² – 4ac > 0 Two equal roots, if b² – 4ac = 0 No real roots, if b² – 4ac < 0

NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions This chapter introduces students to a new topic that is Arithmetic Progression, i.e. AP. The chapter constitutes a total of 4 exercises. In Exercise 5.1, students will find the questions related to representing a situation in the form of AP, finding the first term and difference of an AP, finding out whether a series is AP or not. Exercise 5.2 includes the questions on finding out the nth term of an AP by using the following formula; an = a + (n-1) d

The next exercise i.e., 5.3, contains the questions on finding the sum of first n terms of an AP. The last exercise includes higher-level questions based on AP to enhance students’ analytical and problem-solving skills.

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Dated: 22/Nov/2020

Timing : 10:30 AM to 12:30PM

Test ID: CBSE-XS101

Modes: Offline Classroom 📚✍ / Online 💻

✅Mathematics:

Chapter: Real Number

Topics: Euclid's Division Lemma and Algorithm, HCF of Two Numbers, LCM and HCF by Prime Factorisation, Prime and Composite Numbers,

✅Science:

1) Chemistry:

Chapter: Chemical Reactions and Equations

Topics: Balance Chemical reactions

2) Biology:

Chapter: Life Process

Topics: Nutrition, Autotrophic, Heterotrophics, Nutrition in Amoeba

3) Physics

Chapter: Light

Topics: Reflection of Light, Mirror, Mirror Formula

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NCERT Class 10 Chapter: Real Numbers Exercise 1.1 Use Euclid’s division algorithm to find the HCF of 135 and 225.

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#RealNumbers #Class10Maths

In this lecture I have discussed Number System and Euclid's Division Lemma of NCERT Chapter 1 Real Numbers Class 10 Maths.

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NCERT Solutions for class 10 maths

Class 10th maths is crucial of all the subjects, as it helps in building the foundation of the future technical courses. The ncert solutions for class 10 maths provided comprises of solutions to all the exercises given in CBSE textbook. The expert team at entrencei have keenly evaluated and reviewed the complete set of material. And to help you we have uploaded Maths formula in one page for effective revision .We solely believe in providing the best of ncert solutions for class 10 maths in order to ease the process of learning. In case if you face any issue regarding the material provided, then you can directly reach to our executives.

 The level of education provided by NCERT helps in creating a strong base for the one looking to higher technical studies. the continuous effort of the team at entrencei have led to provide you with an extensive list of chapters solution to ncert solutions for class 10 maths of which chapters are mentioned below:

 Chapter 1 – Real Numbers

This topic of ncert solutions for class 10 maths comprises of extension provide to 9th class. One would be made aware of the intrinsic details of Euclid’s division algorithm, rational numbers. The ncert solutions for class 10 maths provide help in understanding divisibility of integers.

 Chapter 2 – Polynomials

This part of ncert solutions for class 10 maths comprises of four exercises.  All the exercise mentioned deal around determining zeroes of polynomials, quadratic polynomials.

 Chapter 3 – Pair Of Linear Equation In Two Variables

The introduction to this chapter mentioned in ncert solutions for class 10 maths comprises of laying concepts of linear equations in two variables. In this chapter detailed study could be made of the graphical method and algebraic method of solving linear equations. Elimination method, substitution method, cross-multiplication method are explained in exercises format.

 Chapter 4 – Quadratic Equation

This ncert solutions for class 10 maths comprises of methods to find roots of the quadratic equation. The exercises mentioned would comprise of questions related to our day to day life problems. One will study regarding completing the square and factorization method to determine roots of quadratic equations. Nature of roots are the main topics to be studied in this ncert solutions for class 10 maths.

 Chapter 5 – Arithmetic Progressions

This topic of ncert solutions for class 10 maths has minor complex problems related summation of consecutive terms. This topic helps in finding solutions to real-life problems.

 Chapter 6 – Triangles

This chapter consists of questions based upon properties of triangles which are very extensively explained in ncert solutions for class 10 maths provided by us. The main 9 theorems mentioned in it are of main importance with respect to exams.

 Chapter 7 – Coordinate Geometry

This chapter has been holding a very crucial place, as it helps in finding the distance between two coordinates provided. The ncert solutions for class 10 maths to this chapter have been made very entreating to understand for students.

 Chapter 8 – Introduction to Trigonometry

This chapter comprises of determining trigonometric ratios of acute angles of triangles. The ncert solutions for class 10 maths provide for ratios of complementary angles are main topics to be focused upon.

 Chapter 9 – some applications of Trigonometry

This chapter will bring you some new sides of solving mathematics as provided by our team in ncert solutions for class 10 maths.

 Chapter 10 – Circles

Here you will be brought some untouched theorems and formula of the circle.

 Chapter 11 – Construction

Here you will be using ruler and compass to draw some geometric figures. Carving out bisector of angle and triangles construction has been very extensively mentioned in ncert solutions for class 10 maths.

 Chapter 12 - Areas related to Circles

You must be well acquainted with finding areas of different geometric plane figures. The reference of ncert solutions for class 10 maths would the chapter very easy.

 Chapter 13 – Surface Areas and Volumes

Well, this chapter is the continuation of 9th standard. One will be made acquainted with volumes and areas of cubes, cuboid, and cylinders.

 Chapter 14 – Statistics

Here you will be calculating mean, median and mode to grouped data. The problems related to cumulative frequency will also be worked upon.

Chapter 15 – Probability

Students will be made acquainted with the values of probability lying between zero and one.

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NCERT Class 10

Chapter: Real Numbers

Exercise 1.1

Question 1(ii), (iii)

Use Euclid’s division algorithm to find the HCF of 196 and 38220.

Use Euclid’s division algorithm to find the HCF of 867 and 255.

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NCERT Solutions Class 10 Maths Chapter 1

NCERT Solutions Class 10 Maths Chapter 1 NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Mathematics Chapter 1 Real Numbers.

Exercise 1.1

Question 1.

Use Euclid’s division algorithm to find the HCF of:

(i) 135 and 225

(ii) 196 and 38220

(iii) 867 and 255.

Solutions:

(i) Given numbers are 135 and 225.

On applying Euclid’s division algorithm, we have

225 = 135 x 1 + 90

Since the remainder 90 ≠ 0, so again we apply Euclid's division algorithm to 135 and 90, to get

135 = 90 x 1 + 45

Since the remainder 45 ≠ 0, so again we apply Euclid’s division algorithm to 90 and 45, to get

90 = 45 x 2 + 0

The remainder has now become zero, so we stop.

∵ At the last stage, the divisor is 45

∴ The HCF of 135 and 225 is 45.

(ii) Given numbers are 196 and 38220

On applying Euclid’s division algorithm, we have

38220 = 196 x 195 + 0

Since we get the remainder zero in the first step, so we stop.

∵ At the above stage, the divisor is 196

∴ The HCF of 196 and 38220 is 196.

(iii) Given numbers are 867 and 255

On applying Euclid’s division algorithm, we have

867 = 255 x 3 + 102

Since the remainder 102 ≠ 0, so again we apply Euclid’s division algorithm to 255 and 102. to get

255 = 102 x 2 + 51

Since the remainder 51 ≠ 0, so again we apply Euclid’s division algorithm to 102 and 51, to get

102 = 51 x 2 + 0

We find the remainder is 0 and the divisor is 51

∴ The HCF of 867 and 255 is 51.

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