New
New
Year 7

Expressing an integer as a product of its prime factors

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

New
New
Year 7

Expressing an integer as a product of its prime factors

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

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Lesson details

Key learning points

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

Keywords

  • Composite - A composite number is an integer with more than two factors. All integers greater than 1 are either composite or prime

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

  • Unique - Each composite number has a unique product of its prime factors. i.e. there is only one unique way it can be written.

Common misconception

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

Reiterate that the product of prime factors is unique.

Get students to check their solutions on a calculator.
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).

Lesson video

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6 Questions

Q1.
Fill in the missing word in this statement: A number which has exactly 2 factors is called a number.
Correct Answer: prime
Q2.
Which of the following arrays shows that 6 is not a prime number?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q3.
Which of the following is not a prime number?
11
Correct answer: 15
17
19
Q4.
True or false? 31 is a prime number.
Correct answer: True, it has exactly 2 factors, 1 × 31
False, you can make an array of 3 × 11
Q5.
True or false? All odd numbers between 2 and 10 are prime numbers.
True, you cannot make an array with a width of 2
Correct answer: False, 9 has 3 factors
Q6.
Which is the odd one out in this list? 37, 47, 57, 67
37
47
Correct answer: 57
67

6 Questions

Q1.
Fill in the missing word: Integers greater than 1 are either or prime.
Correct Answer: composite
Q2.
What number is missing in this statement? Composite numbers have more than factors
1
Correct answer: 2
3
4
Q3.
What is the missing number in the first step in the process to find prime factors of 12? $$12 = 2 ×$$
Correct Answer: 6, six
Q4.
What is the missing product in this process to find prime factors of 12?
An image in a quiz
Correct answer: 2 × 3
2 + 3
3 + 2
1 × 6
3 + 3
Q5.
Given that 120 = $$2^3\times3\times5$$, which of the following equals 600?
$$2^4\times3\times5$$
Correct answer: $$2^3\times3\times5^2$$
$$2^3\times3^2\times5$$
Q6.
Given that 3600 = $$2^4\times3^2\times5^2$$, which of the following equals 360?
Correct answer: $$2^3\times3^2\times5$$
$$2^2\times3\times5$$
$$2^5\times3^2\times5^3$$