Highest Common Factor
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.
Factors Worksheets/Games
Practice your skills with the following Factors worksheets:
Printable & Online Factors Worksheets
Factor Finder Game
Prime Factorization Game
Highest Common Factor Game
Least Common Multiple Game
How to find the HCF?
Listing Factors Method: (suitable for small numbers)
- List out all the factors of each number
- Select the largest factor that appears in all the lists.
Prime Factorization:
- Use a factor tree to find the prime factors of each numbers.
- Find the prime factors that are common to both numbers and multiply them.
Use repeated division (ladder) method
- Write the numbers for which you want to find the HCF in a horizontal row.
- Find the smallest prime number that divides all the numbers evenly. Write this prime factor to the left of the numbers.
- Divide each number by this common prime factor and write the quotients in a new row below the original numbers.
- Continue steps 2 and 3 with the new row of quotients. Keep dividing by common prime factors until there are no more prime factors that divide all the numbers in the row.
- The HCF is the product of all the prime factors listed on the left side of the ladder (the ones you divided by).
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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