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Lesson 16 of 19
  • Year 7

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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View unit
Lesson 16 of 19
New
New
  • 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

These resources will be removed by end of Summer Term 2025.

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These resources were created for remote use during the pandemic and are not designed for classroom teaching.

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Lesson details

Key learning points

  1. Common factors can be found by comparing the products of their primes.
  2. The highest common factor of two numbers can be found by comparing the prime factorisation of both numbers.
  3. Sometimes a Venn diagram can help identify the highest common factor of two numbers.
  4. 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.


To help you plan your year 7 maths lesson on: Highest common factor, download all teaching resources for free and adapt to suit your pupils' needs...

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
A number is the product of two repeated integers.

Correct Answer: square

Q2.
Write $$2^3\times3\times5^2$$ as an integer.

Correct Answer: 600, six hundred

Q3.
True or false? $$2^5\times3^3\times5$$ is an even integer

False, the exponents are odd
Correct answer: True, it has a factor of 2

Q4.
True or false? $$2\times3\times5^2$$ is a multiple of 10

Correct answer: True, 2 and 5 are both factors
False, $$5^2$$ is 25 and that is not a multiple of 10

Q5.
Which of the following is a multiple of 6?

$$2\times5\times7$$
$$2^3\times5^2\times7$$
Correct answer: $$2^4\times3^2\times5\times7$$
$$3^2\times5\times7^3$$

Q6.
Which of the following is a square number?

$$2^2\times3^2\times5$$
Correct answer: $$2^2\times3^4\times5^6$$
$$2\times3^2\times5$$
$$2^4\times3^2\times5^3$$

Assessment exit quiz

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6 Questions

Q1.
The C in HCF stands for

Correct Answer: common

Q2.
$$7^5$$ is a factor of an integer. Which of the following are also factors of the same integer?

Correct answer: 7
$$7^8$$
Correct answer: $$7^3$$
Correct answer: $$7^2$$
$$7^9$$

Q3.
Which of the following is a factor of $$2^4\times3^2\times5^2$$ and of $$2^3\times3^4\times5$$?

$$2^4\times3^4\times5^2$$
$$2^3\times3^2\times5^2$$
Correct answer: $$2^3\times3^2\times5$$
$$2^2\times3^2\times5^2$$

Q4.
The HCF of 120 and 630 is

An image in a quiz
Correct Answer: 30, thirty

Q5.
The HCF of 42, 60 and 90 is

An image in a quiz
Correct Answer: 6, six

Q6.
The HCF of 36, 54 and 270 is 18. The missing prime factor in the Venn diagram is

An image in a quiz
Correct Answer: 2, two