To find Highest Common Factor by using Prime Factorization Method

To find highest common factor by using prime factorization method is discussed here.

Step I:

Find the prime factorization of each of the given numbers.

Step II:

The product of all common prime factors is the HCF of the given numbers.

Let us consider some of the examples to find highest common factor by using prime factorization method.

1. Find highest common factor (HCF) of 14 and 8 by using prime factorization method.

Solution:

14 = 1 × 2 × 7.

8 = 1 × 2 × 2 × 2.

Common factor of 8 and 14 = 1 and 2.

H.C.F. is the product of lowest powers of factors common to all numbers.

Highest common factor of 8 and 14 = 2.

2. Find highest common factor (HCF) of 9 and 27 by using prime factorization method.

Solution:

9 = 1 × 3 × 3.

27 = 1 × 3 × 3 × 3.

Common factor of 9 and 27 = 1, 3 and 3.

Highest common factor of 9 and 27 = 3 × 3 = 9.

3. Find highest common factor (HCF) of 6 and 16 by using prime factorization method.

Solution:

6 = 1 × 2 × 3.

16 = 1 × 2 × 2 × 2 × 2.

Common factor of 6 and 16 = 2.

Highest common factor of 6 and 16 = 2.

4. Find highest common factor (HCF) of 18 and 24 by using prime factorization method.

Solution:

18 = 1 × 2 × 3 × 3.

24 = 1 × 2 × 2 × 2 × 3.

Common factor of 18 and 24 = 1, 2, 3.

Highest common factor of 18 and 24 = 2 × 3 = 6.

5. Find highest common factor (HCF) of 12 and 56 by using prime factorization method.

Solution:

12 = 1 × 2 × 2 × 3.

56 = 1 × 2 × 2 × 2 × 7.

Common factor of 12 and 56 = 1, 2, 2.

Highest common factor of 12 and 56 = 2 × 2 = 4.

6. Find the HCF of 108 and 132 by prime factorization method.

Solution:

$HCF of 108 and 132$

108 = 2 × 2 × 3 × 3 × 3

132 = 2 × 2 × 3 × 11

Thus, the HCF is 2 × 2 × 3 = 12

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