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      Calculating integers from their prime factor expressions

      Lesson details

      Learning outcome

      I can evaluate a number written as a product of its prime factors.

      Key learning points

      1. Evaluating a product of primes will give a unique positive integer.
      2. It is useful to compare numbers using their prime factor product without evaluating the numbers.
      3. Square numbers can be identified from their product of primes.
      4. Common factors can be found by comparing the products of their primes.

      Keywords

      • Composite number - A composite number is an integer with more than two factors.

      • Product - A product is the result of two or more numbers multiplied together.

      • Prime factors - Prime factors are factors of a number that are, themselves, prime.

      • Exponent - An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication.

      Common misconception

      Identifying if integer is a multiple when its given in its prime factor form.

      Only the bases need to be considered, not the exponents. e.g if it is a multiple of 3 it must be a multiple of 3^2, 3^3, etc.

      Teacher tip

      When working through the factors of 60 and 24 pair the students and get them to give the factor pairs in order, stressing the importance of using a systematic approach. They should take it in turns to give the first one of the pair.

      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.
      Fill in the missing word: Integers greater than 1 are either composite or .

      Correct Answer: prime

      Q2.
      Which of the following shows that 77 is a composite number?

      77 × 1
      Correct answer: 7 × 11
      1 × 77
      Correct answer: 11 × 7

      Q3.
      What is the missing number in the first step in the process to find prime factors of 75? $$75 = 3 \times $$

      Correct Answer: 25, twenty-five

      Q4.
      What is the missing product in this process to find prime factors of 75?

      An image in a quiz
      15 + 10
      20 + 5
      1 × 25
      Correct answer: 5 × 5

      Q5.
      Given 120 = $$2^3\times3\times5$$, which of the following equals 360?

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

      Q6.
      Given 120 = $$2^3\times3\times5$$, which of the following equals 60?

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

      6 Questions

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

      Correct Answer: repeated, same, repeat, identical

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

      Correct Answer: 60, sixty

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

      Correct answer: True, it has a factor of 2
      False, the exponent is odd

      Q4.
      True or false? $$3\times5^2$$ is a multiple of 10

      True, 5 is a factor and 10 is a multiple of 5
      Correct answer: False, to be a multiple of 10 it must have a factor of 2 and 5

      Q5.
      Which of the following is not a multiple of 6?

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

      Q6.
      Which of the following is a square number?

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

      To help you plan your 7 maths lesson on: Calculating integers from their prime factor expressions, download all teaching resources for free and adapt to suit your pupils' needs...