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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.

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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

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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.

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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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: $$2^2\times3^4\times5^6$$

$$2\times3^2\times5$$

$$2^4\times3^2\times5^3$$

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

Correct Answer: 30, thirty

Q5.

The HCF of 42, 60 and 90 is

Correct Answer: 6, six

Q6.

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

Correct Answer: 2, two