# NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers: The chapter starts with Euclid’s Division Lemma and uses this concept to find the HCF of given numbers. The concept of Euclid's Division Lemma is, given two positive integers a and b can be expressed as a=bq+r such that r is greater than or equal to zero and less than or equal to b. Suppose the given numbers are 455 and 42 then we can write $455=42\times10+35$. How can we find the HCF of 455 and 42 using Euclid’s Division Lemma?

we can write

$455=42\times10+35$

$42=35\times1+7$

$35=7\times5+0$

Now the remainder is zero and we will say that the HCF of 455 and 42 is 7. Can you find out the logic behind this? Can you give a real-life example where we can use the concepts of HCF? Here is a question which is taken from NCERT: A sweet seller has 420 Kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray. What is the number of that can be placed in each stack for this purpose? The solution is the HCF of 420 and 130.

The NCERT Solutions for Class 10 Maths Chapter 1 exercise 1 mainly focus on how to find HCF using Euclid’s Division Lemma and the next session of NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers  introduces the fundamental theorem of arithmetic, that is any composite number can be written as the product of powers of primes. That is

$\\42=2\times3\times7\\1001=7\times11\times13$

The second exercise of  NCERT Solutions of this chapter is mainly based on the concept of the fundamental theorem of arithmetic and the relation that the product of LCM and HCF of given two numbers equal to the product of the numbers. The next session of the NCERT Solutions for Class 10 of this chapter explains the proof of irrational numbers using the fundamental theorem of arithmetic. The last topic of the chapter explains how to know that a given rational number is of the form p/q where p and q are co-primes and q not equal to zero.

## The main topics of NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers are given below:

1.1 Introduction

1.2 Euclid’s Division Lemma

1.3 The Fundamental Theorem of Arithmetic

1.4 Revisiting Irrational Numbers

1.5 Revisiting Rational Numbers and Their Decimal Expansions

NCERT Solutions for Class 10 Maths Chapter 1 consist of 4 exercises, out of which one is optional. Practicing all six exercises is mandatory. Below are the detailed of Class 10 NCERT solutions:

## NCERT Solutions for Class 10 Maths - Chapter-wise

 Chapter No. Chapter Name Chapter 2 Polynomials Chapter 3 Pair of Linear Equations in Two Variables Chapter 4 Quadratic Equations Chapter 5 Arithmetic Progressions Chapter 6 Triangles Chapter 7 Coordinate Geometry Chapter 8 Introduction to Trigonometry Chapter 9 Some Applications of Trigonometry Chapter 10 Circles Chapter 11 Constructions Chapter 12 Areas Related to Circles Chapter 13 Surface Areas and Volumes Chapter 14 Statistics Chapter 15 Probability

## NCERT Solutions for Class 10 - Subject Wise

 NCERT Solutions for Class 10 Maths NCERT Solutions for Class 10 Science