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Questions and Solutions for NCERT Class 6th Mathematics Chapter 3 – Playing with Numbers – Exercise 3.6
1. Find the HCF of the following numbers :
(a) 18, 48
Sol: Factors of 18 = 2 × 3 × 3
Factors of 48 = 2 × 2 × 2 × 2 × 3
HCF of 18 and 48 = 2 × 3 = 6
(b) 30, 42
Sol: Factors of 30 = 2 × 3 × 5
Factors of 42 = 2 × 3 × 7
HCF of 30 and 42 = 2 × 3 = 6
(c) 18, 60
Sol: Factors of 18 = 2 × 3 × 3
Factors of 60 = 2 × 2 ×3 × 5
HCF of 18 and 60 = 2 × 3 = 6
(d) 27, 63
Sol: Factors of 27 = 3 × 3 × 3
Factors of 63 = 3 × 3 × 7
HCF of 27 and 63 = 3 × 3 = 9
(e) 36, 84
Sol: Factors of 36 = 2 × 2 × 3 × 3
Factors of 84 = 2 × 2 ×3 × 7
HCF of 36 and 84 = 2 × 2 × 3 = 12
(f) 34, 102
Sol: Factors of 34 = 2 × 17
Factors of 102 = 2 × 3 × 17
HCF of 34 and 102 = 2 × 17 = 34
(g) 70, 105, 175
Sol: Factors of 70 = 2 × 5 × 7
Factors of 105 = 3 × 5 × 7
Factors of 175 = 5 × 5 × 7
HCF of 70, 105 and 175 = 5 × 7 = 35
(h) 91, 112, 49
Sol: Factors of 91 = 7 × 13
Factors of 112 = 2 × 2 × 2 × 2 × 7
Factors of 49 =7 × 7
HCF of 91, 112 and 49 = 7
(i) 18, 54, 81
Sol: Factors of 18 = 2 × 3 × 3
Factors of 54 = 2 × 3 × 3 × 3
Factors of 81 = 3 × 3 × 3 × 3
HCF of 18 , 54 and 81 = 3 × 3 = 9
(j) 12, 45, 75
Sol: Factors of 12 = 2 × 2 × 3
Factors of 45 = 5 × 3 × 3
Factors of 75 = 3 × 5 × 5
HCF of 12 , 45 and 75 = 3
2. What is the HCF of two consecutive
(a) numbers?
Ans: HCF of two consecutive numbers is 1
Example: HCF of 14 (14 = 2 * 7) and 15 (15 = 3 * 5) is 1
(b) even numbers?
Ans: HCF of two consecutive numbers is 2
Example: HCF of 6 (6 = 2 * 3) and 8 (8 = 2 * 2 * 2) is 2
(c) odd numbers?
Ans: HCF of two consecutive odd numbers is 1
3. HCF of co-prime numbers 4 and 15 was found as follows by factorisation :
4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF?
Ans: No, the correct answer is 1.
You can find the solutions for Class 6 Mathematics previous exercises from here
- Playing with Numbers – Exercise 3.5 Solutions
- Playing with Numbers – Exercise 3.4 Solutions
- Playing with Numbers – Exercise 3.3 Solutions
- Playing with Numbers – Exercise 3.2 Solutions
- Playing with Numbers – Exercise 3.1 Solutions
- Whole Numbers – Exercise 2.3 Solutions
- Whole Numbers – Exercise 2.2 Solutions
- Whole Numbers – Exercise 2.1 Solutions
- Knowing Our Numbers Solutions Exercise 1.3 Solutions
- Knowing Our Numbers Solutions Exercise 1.2 Solutions
- Knowing Our Numbers Solutions Exercise 1.1 Solutions
