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      Checking and securing understanding of prime factorisation

      Lesson details

      Learning outcome

      I can write any positive integer uniquely as a product of its prime factors.

      Key learning points

      1. Every positive integer can be broken down into prime factors.
      2. Every positive integer can be written as a product of its prime factors.
      3. Prime factor products can be simplified by using index notation.

      Keywords

      • Product of primes - Expressing a number as a product of primes means writing it uniquely as a product of its factors that are prime numbers.

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

      • Prime factorisation - Prime factorisation is a method to find the prime factors of a given integer.

      Common misconception

      Use of addition instead of multiplication when the decomposing the number.

      Reiterate that the product of prime factors is unique. This should also be helped when setting the decomposition out as products rather than just a 'tree'.

      Teacher tip

      Challenge pupils to write their own 'Who am I?' problems with unique answers. They can then swap and try to find each others numbers.

      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.
      Calculate 0.25 × 0.94, giving your answer as a decimal.

      Correct Answer: 0.235

      Q2.
      Which of these is equivalent to 0.8?

      $$\frac{8}{100}$$
      Correct answer: $$\frac{4}{5}$$
      $$\frac{2}{10}$$

      Q3.
      Calculate 3.25 × 7.94, giving your answer as a decimal.

      Correct Answer: 25.805

      Q4.
      Calculate -0.3 + 9.1, giving your answer as a decimal.

      Correct Answer: 8.8

      Q5.
      Calculate 0.28 ÷ 0.04, giving your answer as a decimal.

      Correct Answer: 7

      Q6.
      Convert 3.4 into a mixed number.

      $$\frac{34}{10}$$
      Correct answer: $$3\frac{2}{5}$$
      $$\frac{34}{100}$$

      6 Questions

      Q1.
      What number is written as $$2 × 5^2 × 19$$ as a product of its prime factors?

      Correct Answer: 950

      Q2.
      What number is written as $$2 × 5 × 31$$ as a product of its prime factors?

      Correct Answer: 310

      Q3.
      What number is written as $$3 × 5 × 11$$ as a product of its prime factors?

      Correct Answer: 165

      Q4.
      Which of these is a prime factor of 10905?

      2
      Correct answer: 5
      8

      Q5.
      Which of these is the prime factorisation of 450?

      $$2 × 3 × 5$$
      $$2 × 3^2 × 5$$
      Correct answer: $$2 × 3 ^2× 5^2$$

      Q6.
      Which of these is the prime factorisation of 539?

      Correct answer: $$7^2 × 11$$
      $$2^3 × 7^2 $$
      $$3^3 × 7^2 $$

      To help you plan your 10 maths lesson on: Checking and securing understanding of prime factorisation, download all teaching resources for free and adapt to suit your pupils' needs...