Lesson 1, Topic 3
In Progress

# Highest Common Factors (HCF)

Lesson Progress
0% Complete

The highest common factors (HCF) of two or more numbers is the greatest of the factors common to them.

There are different methods of finding H.C.F. of two or more numbers. 2 of those methods are;

1. Short division method

2. Prime Factorization Method

Example 1

Find the HCF of

a. 12 and 16

b. 18 , 27 and 36

c.

2 x 2 x 3 x 5 x 7

2 x 2 x 2 x 2 x 7

d.

22 x 33 x 5

23 x 32 x 52

Solution

a. 12 and 16

### Method 1: divide each number by common prime factors (Short Division Method)

• Write the numbers in individual rows.
• Divide the numbers by common prime factors.
• Factorisation stops when we reach prime numbers which cannot be further divided.
• HCF is the product of all the common factors.

Hence, the common factors are 2, and 2.

HCF of 12 and 16 = 2 × 2 = 4

### Method 2:Prime Factorization Method

Express each number as a product of its prime factors and multiply their common prime factors.

HCF  =  2 x 2 = 4

b. 18, 27 and 36

Method 1

HCF =  3 x 3 = 9

Method 2

18 = 2   x    3   x   3

27 = 3   x    3     x    3

36 = 2   x   2   x  3  x   3

HCF  = 3 x 3 = 9

c.

2 x 2 x 3 x 5 x 7

2 x 2 x 2 x 2 x 7

HCF   =   2 x  2

=   4

d.

22 x 33 x 5

23  x  32  x  52  x 7

In this case, the easiest way is to compare powers of the same base. The one with the lowest power is a common factor.

HCF  =   22   x  32   x  5

=   4  x 9 x 5  =  180

Note: 22  and 23 The index  (power) ‘2’ is  lower than 3

33 and 32 The index ‘2’ is lower than 3

51 and 52 The index ‘1’ is lower than 2

22   is less than(<)   23

32  is less than(<)  33

51   is less than(<)  52 error: