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# How to Find HCF by Prime Factorization Method?

August 19, 2022 written by Azhar Ejaz

There are many ways to determine the highest common factor of the given numbers. For every method, the result to the HCF of the numbers would always be the same. There are three different ways to calculate the HCF of two or more numbers: the greatest common factor by a listing method, the highest common factor by division method, and the HCF by prime factorization method in this article how to find HCF by prime factorization.

## HCF by Prime Factorization Method

In order to calculate the HCF of numbers by the prime factorization method, we use the following steps. Let us explain this method using the example given below.

Step 1: calculate the common prime factors of the given numbers.

Step2: Then, product these common prime factors to obtain the HCF of those numbers.

For example: calculate the highest common factor HCF of 24 and 36 by using the prime factorization method

Solution: find the highest common factor HCF of 24 and 36

The prime factors of 24 = 2 × 2 × 2 × 3

and the prime factors of 36 = 2×2 × 3 × 3. Now, the HCF of 24 and 36 will be the multiplying of the common prime factors, which are,2, 2,  and 3. So, HCF of 24 and 36= 2 × 2 × 3 = 12

For example: calculate the highest common factor HCF of 32 and 80 by using the prime factorization method

Solution: find the highest common factor HCF of 32 and 80

The prime factors of 32=2x2x2x2x2

The prime factors of 80=2x2x2x2x5

Common prime factors of 32 and 80=2x2x2x2

Now, the HCF of 32 and 80 will be multiplied of the common prime factors

2x2x2x2=16

HCF (32,80)=16

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