Accessable NCERT class 6 mathematics text book prepared by Prof. T K Bansal.

We can find the common factors of any two numbers. We now try to find the highest of these common factors.

What are the common factors of 12 and 16? They are 1, 2 and 4.
What is the highest of these common factors? It is 4.
What are the common factors of 20, 28 and 36? They are 1, 2 and 4 and again 4 is highest of these common factors.

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

It is also known as Greatest Common Divisor (GCD).

The HCF of 20, 28 and 36 can also be found by prime factorisation of these numbers as follows:

Thus, 20 = 2 × 2 × 5
28 = 2 × 2 × 7
36 = 2 × 2 × 3 × 3

The common factor of 20, 28 and 36 is 2(occuring twice). Thus, HCF of 20, 28 and 36 is 2 × 2 = 4.

EXERCISE 3.6

Q1. 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

A1.
(a) 6
(b) 6
(c) 6
(d) 9
(e) 12
(f) 34
(g) 35
(h) 7
(i) 9
(j) 3

Q2. What is the HCF of two consecutive
(a) numbers?
(b) even numbers?
(c) odd numbers?

A2.
(a) 1
(b) 2
(c) 1

Q3. HCF of co-prime numbers 4 and 15 was found as follows by factorization :
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?

A3. No ; the HCF is 1