Lesson 1, Topic 3
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# Highest Common Factors (HCF)

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The highest common factor (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 ofÂ

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 x 7

Solution

a. 12 and 16

### Method 1: (Short Division Method)

Applying this method, we divide each number by common prime factors. The steps are as follows:

• 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 Ã— 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 Â  xÂ  Â  3 Â  x Â  3
27 = 3 Â  xÂ  Â  3 Â  Â  xÂ  Â  3
36 = 2 Â  x Â  2 Â  xÂ  3Â  x Â  3

HCF  = 3 x 3 = 9

c.

2 x 2 x 3 x 5 x 7 Â  Â  Â  Â
2 x 2 x 2 x 2 x 7

HCF   =   2 x  2

=   4

d.

22 x 33 x 5
23Â  xÂ  32Â  xÂ  52Â  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

Â Note:
22Â  and 23 The indexÂ  (power) â€˜2â€™ isÂ  lower than 3
33 and 32 The index â€˜2â€™ is lower than 3
51 and 52 The index â€˜1â€™ is lower than 2
22 Â  is less than (<) Â  23Â
32Â  is less than (<)Â  33Â
51 Â  is less than (<)Â  52

#### Responses

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