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Year 10
Higher

Checking and securing understanding of prime factorisation

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

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New
New
Year 10
Higher

Checking and securing understanding of prime factorisation

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

Download all resources
Share activities with pupils

Lesson details

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.

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'.

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.

Challenge pupils to write their own 'Who am I?' problems with unique answers. They can then swap and try to find each others numbers.
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.
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: $$3\frac{2}{5}$$
$$\frac{34}{100}$$

Exit quiz

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