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Toggle## Class 6, Maths, Chapter 3, Exercise 3.6 Solutions

**Q.1. Find the HCF of the following numbers :**

**(a) 18, 48**

**(b) 30, 42 **

**(c) 18, 60 **

**(d) 27, 63**

**(e) 36, 84 **

**(f) 34, 102 **

**(g) 70, 105, 175**

**(h) 91, 112, 49 **

**(i) 18, 54, 81 **

**(j) 12, 45, 75**

**Ans:**

*The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors*

**Q.2. What is the HCF of two consecutives**

**(a) numbers? **

**(b) even numbers? **

**(c) odd numbers?**

**Ans:**

**(a) **The HCF of two consecutive numbers is 1

Example(i): The HCF of 2 (2=1×2) and 3 (3 = 1×3) is 1.

Example(ii): The HCF of 15 (15 = 1 x 3 x 5) and 16 (16 = 1x2x2x2x2) is 1.

(b) The HCF of two consecutive even numbers is 2

Examples:

(a) HCF of 2 (2= 1×2) and 4 (4= 1x 2 x 2) is 2.

(b) HCF of 6 (6 = 1×2 x 3) and 8 (8 = 1 x 2 x 2 x 2) is 2

(c) The HCF of two consecutive odd numbers is 1

Example: The HCF of 3 (3 = 1×3) and 5 (1×5) is 1

**Q.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 answer is not correct. The correct HCF (Highest Common Factor) of co-prime numbers 4 and 15 is 1.

Co-prime numbers are two numbers that do not have any common factor except 1.

In this case,

Prime factors of 4 = 2 x 2,

Prime factors of 15 = 3 x5.

As there is no common prime factor between them, the HCF of 4 and 15 is 1.

So, the correct answer is HCF (4, 15) = 1.

## NCERT Solutions For Class 6 Maths, Chapter 3 Playing With Numbers (All Exercises)

**Class 6, Maths, Chapter 3, Playing With Numbers **

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.1**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.2**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.3**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.4**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.5**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.6** **← You are here**

**Class 6, Maths, Chapter 3, Playing With Numbers, Exercise 3.7**