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      Lesson details

      Learning outcome

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

      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.

      Teacher tip

      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.

      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

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

      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

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