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Year 7

Calculating integers from their prime factor expressions

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

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New
New
Year 7

Calculating integers from their prime factor expressions

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

Download all resources
Share activities with pupils

Lesson details

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.

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.

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.

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.
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.
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: $$2^2\times3\times5$$

Exit quiz

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