Highest Common Factor

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Examples, examples, and videos to help GCSE Maths students learn how to find the highest common factor (HCF).

What is Highest Common Factor (HCF)?
The Highest Common Factor of two or more numbers is the largest number that can divide the numbers without any remainder. The highest common factor is also called the Greatest Common Factor (GCF).

The following diagrams show the methods that can be used to find the Highest Common Factor. Scroll down the page for more examples and solutions on how to find the Highest Common Factor.

Highest Common Factor

How to find the HCF?
There are various methods to find the HCF. Here are some of them:

  1. List out all the factors of each number and select the largest factor that is common to all the lists.
  2. Use prime factors or factor trees.
  3. Use division (ladder) method.

GCSE Maths, Finding Highest Common Factors by listing the factors

Highest Common Factor from prime factors
How to find the highest common factor (HCF) of two number using the product of primes

Greatest Common Factor
This video reviews how to find the Greatest Common Factor (GCF) of a pair of numbers using the upside down division (ladder) method.

Example: Determining the Greatest Common Factor
This video provides two examples of determining the greatest common factor by using prime factorization.

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