Highest common factor

I can use the prime factorisation of two or more positive integers to efficiently identify the highest common factor.

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Year 7

Highest common factor

I can use the prime factorisation of two or more positive integers to efficiently identify the highest common factor.

Download all resources

Share activities with pupils

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Lesson details

Key learning points

Common factors can be found by comparing the products of their primes.
The highest common factor of two numbers can be found by comparing the prime factorisation of both numbers.
Sometimes a Venn diagram can help identify the highest common factor of two numbers.
The highest common factor of more than two numbers can be found using prime factorisation.

Keywords

Prime factorisation - a method to find the prime factors of a given integer
Highest common factor - The highest common factor of two or more integers  which can be divided by all other possible common factors
HCF - an abbreviation for highest common factor

Common misconception

Common factors are put into the intersection of the Venn diagram twice instead of once.

Encourage students to check that the product of the factors in each set is the correct integer.

When introducing the idea of putting the prime factors into a Venn diagrams get the students to this first on a mini whiteboard. This will give you the opportunity to identify students who might need support with using a Venn diagram.