## NCERT Exercise 3.6 solution class six math

Question (1) Find the HCF of the following numbers:

(a) 18, 48

**Solution**

The prime factors of 18 = 2 × 3 × 3

The prime factors of 48 = 2 × 2 × 2 × 2 × 3

Thus, the HCF of 18 and 48 = 2 × 3 = 6 **Answer**

(b) 30, 42

**Solution**

The prime factors of 30 = 2 × 3 × 5

The prime factors of 42 = 2 × 3 × 7

Thus, the HCF of 30 and 42 = 2 × 3 = 6 **Answer**

(c) 18, 60

**Solution**

The prime factors of 18 = 2 × 3 × 3

The prime factors of 60 = 2 × 2 × 3 × 5

Thus, the HCF of 18 and 60 = 2 × 3 = 6 **Answer**

(d) 27, 63

**Solution**

The prime factors of 27 = 3 × 3 × 3

The prime factors of 63 = 3 × 3 × 7

Thus, the HCF of 27 and 63 = 3 × 3 = 9 **Answer**

(e) 36, 84

**Solution**

The prime factors of 36 = 2 × 2 × 3 × 3

The prime factors of 84 = 2 × 2 × 3 × 7

Thus, the HCF of 18 and 48 = 2 × 2 × 3 = 12 **Answer**

(f) 34, 102

**Solution**

The prime factors of 34 = 2 × 17

The prime factors of 102 = 2 × 3 × 17

Thus, the HCF of 18 and 48 = 2 × 17 = 34 **Answer**

(g) 70, 105, 175

**Solution**

The prime factors of 70 = 2 × 5 × 7

The prime factors of 105 = 3 × 5 × 7

The prime factors of 175 = 5 × 5 × 7

Thus, the HCF of 70, 105 and 175 = 5 × 7 = 35 **Answer**

**Question (2)** What is the HCF of two consecutive

(a) numbers?

**Answer**

The HCF of two consecutive numbers = 1

**Example (a)**

HCF of 5 and 6

The prime factor of 5 = 5

The prime factor of 6 = 2 × 3

Now since no common factors present between 5 and 6, thus the HCF = 1

**Example (b)**

HCF of 14 and 15

The prime factor of 14 = 2 × 7

The prime factor of 15 = 3 × 5

Now since no common factors present between 14 and 15, thus the HCF = 1

What is the HCF to two consecutive (b) even numbers?

**Answer**

The HCF of two consecutive even numbers = 2 **Answer**

**Example (a)**

HCF of two consecutive even numbers 6 and 8

The prime factors of 6 = 2 × 3

The prime factors of 8 = 2 × 2 × 2

Thus, HCF of 6 and 8 = 2 **Answer**

**Example (b)**

HCF of two consecutive even numbers 28 and 30

The prime factors of 28 = 2 × 2 × 7

The prime factors of 30 = 2 × 3 × 5

Thus, HCF of 28 and 30 = 2 **Answer**

What is the HCF to two consecutive (c) Odd numbers?

**Answer**

The HCF of two consecutive odd numbers = 1 **Answer**

**Example (a)**

HCF of two consecutive odd numbers 5 and 7

The prime factors of 4 = 5 (Because 5 is a prime number)

The prime factors of 7 = 7 (Because 7 is a prime number)

Now since there is no common factor between 4 and 7, thus the HCF of 4 and 7 = 1 **Answer**

**Example (b)**

HCF of two consecutive odd numbers 25 and 27

The prime factors of 25 = 5 × 5

The prime factors of 27 = 3 × 3 × 3

Now since there is no common factor between 25 and 27, thus the HCF of 25 and 27 = 1 **Answer**

**Question (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

**Answer**

If there is no common prime factor between two number, then the HCF of such two numbers = 1

Thus, the given answer 0 in not correct.

The HCF of given numbers = 1 **Answer**