How to find the Highest common factor of Numbers

The highest common factor is the highest factor that divides exactly into all the given numbers. The Highest common factor (HCF) is also called the Greatest common factor (GCF)

How to find the Highest common factor (HCF) of Numbers

There are two ways of finding the Highest common factor (HCF) of numbers which have been discussed in this article.

• using factors and products of primes

Steps in finding the Highest common factor using factors

To find the Highest common factor of given numbers, follow the steps below:

Step1: list down all the factors of each of the given numbers. The factor of a whole number is a whole number that divides exactly into it and gives a whole number as an answer. For instance 15÷3 = 5. In this case, 3 and 5 are factors of 15.

Step2: pick out the common factors that have to occur in the factors of each of the numbers.

Step3: The Highest factor in the common factors is the HCF of the given numbers.

Let’s go straight into looking at examples under this method.

Example 1. Find the Highest common factor (HCF) or (GCF) of 6, 12, and 24.

answer: list all the factors of 6, 12 and 24

factors of 6 = {1,2,3,6}

factors of 12= {1,2,3,4,6,12}

factors of 24= {1,2,3,4,6,8,12,24}

Common factors of 6,12, and 24={1,2,3,6}

The highest factor in the common factors is 6. Hence the Highest common factor (HCF) of 6, 12, and 24 is 6.

This is pretty good, right?

let’s turn our attention to finding the Highest common factor using the product of primes.

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Steps in finding the Highest common factor using the product of primes

To find the Highest common factor (HCF) of given numbers follow the steps below.

Step1: write the given numbers as a product of primes in full or (in index notation form)

Step2: pick out the factors common to all the given numbers and Multiply them.

Step3: If there are in index notation form, take the common factors with the smallest power and Multiply them.

Example 1: Find the Highest common factor of 12, 18, and 30.

answer: write the numbers as a product of primes

12=2×2×3

18=2×3×3

30=2×3×5

The prime numbers common to the product of primes of 12, 18, and 30 are 2, and 3.

Hence the Highest common factor (HCF) of 12, 18, and 30 is 2×3=6.

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