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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
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

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.

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.

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

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
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