# How to Find HCF by Prime Factorization Method?

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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