NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.1
NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.1 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 1 Real Number Exercise 1.1

## NCERT Solutions for Class 10 Maths Exercise 1.1

Ex 1.1 Class 10 Maths Question 1.
Use Euclid’s Division Algorithm to find the HCF of:

(i) 135 and 225(ii) 196 and 38220

(iii) 867 and 255

Ex 1.1 Class 10 Maths Question 2.
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
Ex 1.1 Class 10 Maths 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 marchEx 1.1 Class 10 Maths Question 4.
Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.
Ex 1.1 Class 10 Maths Question 5.
Use Euclid’s Division Lemma to show that the cube of any positive integer is either of the form 9m, 9m + 1 or 9m + 8.

### NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Exercises

Exercise 1.1 of NCERT solutions for class 10 maths chapter 1 Real Numbers is the first exercise of Chapter 1 of Class 10 Maths. Real Numbers is introduced in Class 9 and this is discussed further in detail in Class 10 by studying Euclid’s division Algorithm. The exercise discusses the divisibility of integers. The divisibility of integers using Euclid’s division algorithm says that any positive integer a can be divided by another positive integer b such that the remainder will be which is smaller than b.

Euclid’s Division Algorithm – It includes 5 questions based on Theorem 1.1 – Euclid’s Division Lemma.

Key Features of NCERT Solutions for Class 10 Maths Chapter 1- Real Number Exercise 1.1 Page number 7

These NCERT Solutions help you solve and revise all questions of Exercise 1.1.

After going through the stepwise solutions given by our subject expert teachers, you will be able to score more marks.

• It helps in scoring well in Maths in exams.
• It follows NCERT guidelines which help in preparing the students accordingly.
• It contains all the important questions from the examination point of view.
• Real Numbers Class 10 Maths Objectives

The students will be able to ;

prove Euclid’s Division Lemma

state fundamental theorem of arithmetic

find HCF and LCM using prime factorization

establish the given number as an irrational number

conclude the decimal expansion of a rational number is either terminating or non-terminating repeating.

### Chapter 1 Class 10 Maths Real Numbers Summary

We have studied the following points:

1. Euclid’s Division Lemma: Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r where 0 = r = b.

2. Euclid’s Division Algorithm: According to this, which is based on Euclid’s division lemma, the HCF of any two positive integers a and b with a > b is obtained as follows:

Step 1 Apply the division lemma to find q and r where a = bq + r, O = r < b.

Step 2 If r = 0, the HCF is b . If r? 0 apply Euclid Lemma to b and r

Step 3 Continue the process until the remainder is zero. The divisor at this stage will be HCF (a, b). Also HCF (a, b) = HCF (b, r)

3. The Fundamental Theorem of Arithmetic: Every composite number can be expressed (factorized) as a product of primes and this factorization is unique, apart from the order in which the prime factors occur.

We hope the NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers Ex 1.1, help you. If you have any query regarding Maths NCERT Solutions Chapter 1 Real Numbers Exercise 1.1, drop a comment below and we will get back to you at the earliest.

NCERT Solutions Class 10 Maths Chapter 1 Real Numbers Exercise 1.1 are provided here. These solutions are prepared by our subject expert faculty to help students in their Class 10 first term exam preparations. These experts review these NCERT Maths Solutions chapter wise, so as to help students to solve the problems easily while using it as a reference. They also focus on preparing the NCERT Solutions for these exercises in such a way that it is easy to understand for the students. The first exercise in Real Numbers- Exercise 1.1 explains the divisibility of integers using Euclid’s Division Algorithm. They provide a detailed and stepwise explanation of each answer to the questions given in the exercises in the NCERT textbook for Class 10. The solutions are always prepared by following NCERT guidelines so that it should cover the whole syllabus accordingly. These are very helpful in scoring well in examinations.

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