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      Securing understanding of factors, multiples, squares and cubes

      Lesson details

      Learning outcome

      I can use the multiplication tables to identify factors and multiples.

      Key learning points

      1. Multiplication tables can be used to find multiples of a number.
      2. Multiplication tables can be used to find factor pairs of a number.
      3. Multiplication tables can be used to identify multiples of a number.
      4. Multiplication tables can be used to identify factors of a number.

      Keywords

      • Multiple - A multiple is the product of a number and an integer.

      • Numerical factor - A numerical factor is a factor that is an integer.

      Common misconception

      All factors of all integers will appear in a 12 by 12 times table grid.

      It is not possible to identify all factors of 24 using a 12 by 12 times table grid.

      Teacher tip

      Get students to find all the factors of 100 from a 12 by 12 grid. They will not be able to find the factor pair 1 and 100. The multiplication grid needs to be big enough to find all of the factors of an integer.

      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 numerical is an integer which exactly divides another integer.

      Correct Answer: factor

      Q2.
      Which of the following is a multiple of 7 ?

      20
      Correct answer: 21
      22
      24
      25

      Q3.
      How many multiples of 5 are there?

      1
      10
      100
      Correct answer: infinite

      Q4.
      A __________ number is the product of two repeated integers.

      cube
      product
      prime
      sum
      Correct answer: square

      Q5.
      Which of the following is a factor of 36?

      8
      Correct answer: 12
      72
      108

      Q6.
      Work out the unknown number: "I am less than 100. I am a cube number. I am a factor of 24. I am even."

      Correct Answer: 8, eight

      6 Questions

      Q1.
      __________ and __________ are inverse concepts.

      Correct answer: Factors and multiples
      Squares and cubes
      Decimals and fractions

      Q2.
      Given the calculation $$ 8\times 5 = 40 $$, select the correct statement:

      40 is a factor of 8 and 5
      40 is a square number
      8 and 5 are multiples of 40
      Correct answer: 8 and 5 are factors of 40

      Q3.
      What number is a factor of every integer except zero?

      Correct Answer: 1, one

      Q4.
      List all the factors of 5. Use the multiplication grid to help you.

      An image in a quiz
      5, 10, 15, 20, 25, 30, 35, 40
      Correct answer: 1, 5
      1, 2, 4, 8
      Not possible as there are infinite number of factors of 5

      Q5.
      List all the multiples of 8. Use the multiplication grid to help you.

      An image in a quiz
      1, 2, 4, 8
      8, 16, 24, 32, 40, 48, 48, 56, 64
      Correct answer: Not possible as there are an infinite number of multiples of 8

      Q6.
      Identify if the statement is sometimes true, always true or never true. "A multiple of a number is bigger than its highest factor."

      Correct answer: Sometimes
      Always
      Never

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