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

NCERT solutions for class 10 maths chapter 1 exercise 1.1 Real Numbers is based on the concept of Euclid’s Division algorithm. The questions in this exercise are related to finding the properties of numbers based on the algorithm. It also deals with the topic of finding the HCF of positive integers using the division lemma. If we have to obtain the HCF of two positive integers, say c and d, the first step is to apply Euclid’s division lemma, to c and d. So, we find whole numbers, q, and r such that c = dq + r. Next, if r = 0, then d is the HCF of c and d however, if r ≠ 0, then we apply the division lemma to d and r. Finally, we continue the process till the remainder is zero indicating that the divisor at this stage will be the required HCF. Most of the questions in this NCERT solutions class 10 maths chapter 1 exercise 1.1 are in the word-problem format.

Euclid’s division lemma/algorithm has many applications as it helps in finding the properties of numbers. Despite the fact that Euclid’s Division Algorithm is mentioned only for positive integers, it can be at times applicable to all integers except zero. This exercise has a total of 5 questions, of which three are short and two long answer type questions. The Class 10 Maths NCERT Solutions Chapter 1 exercise 1.1 Real Numbers are available in a scrollable PDF format given below :

**☛** Download NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.1

**Exercise 1.1 Class 10 Chapter 1 **

### More Exercises in Class 10 Maths Chapter 1

- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.2
- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.3
- NCERT Solutions Class 10 Maths Chapter 1 Ex 1.4

## NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.1 Tips

NCERT solutions class 10 maths chapter 1 exercise 1.1 Real Numbers will help the students understand the applications of Euclid’s division lemma through the questions. The only point to remember is that kids should religiously follow the steps to compute the HCF using this lemma. If they deviate it could produce the wrong results. Further, students can verify their answers using some other faster method for finding the HCF such as prime factorization.

NCERT solutions for class 10 maths chapter 1 exercise 1.1 covers the concept of division lemma which states that ‘for any positive integers a and b, we can find unique integers q and r such that a= bq+r’. If you look closely, this theorem can be seen as a restatement of the division where a is the dividend, b is the divisor, q is the quotient, and r is the remainder. This concept is also proved in a detailed way in the NCERT solutions class 10 maths chapter 1 exercise 1.1 with the help of which students can solve all associated problems.

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## NCERT Class 10 Maths Video Solutions Chapter 1 Exercise 1.1

NCERT Videos for Class 10 Maths Chapter 1 Exercise 1.1 | |
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Question 1 | Question 4 |

Question 2 | Question 5 |

Question 3 |