Home / Subjects / Mathematics
➗ Mathematics

Factors, Multiples and Prime Numbers Explained

Learn what factors, multiples and prime numbers are, how to list them and how to test whether a number is prime, with worked examples.

  • ⏱ 3 min read
  • ✏️ 3 worked examples
  • 🎯 5 practice questions
  • 📶 Beginner
KS3GCSEMiddle SchoolHigh School
Start practice questionsDownload PDF

Curriculum fit: GCSE Maths Number (Foundation and Higher). US: Grade 6 number theory.

On this page

What Is It?

A factor of a number divides into it exactly. The factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is what you get when you multiply a number by a whole number, so multiples of 4 are 4, 8, 12, 16 and so on.

A prime number has exactly two factors: 1 and itself. The first primes are 2, 3, 5, 7, 11 and 13. The number 1 is not prime because it has only one factor.

1 × 122 × 63 × 41234612
Factors come in pairs that multiply to give the number. The factors of 12 are 1, 2, 3, 4, 6 and 12.

Key Formulas and Ideas

  • Factor pairs of n multiply to give n.
  • A number is divisible by 2 if it ends in an even digit, by 5 if it ends in 0 or 5, and by 3 if its digits add to a multiple of 3.
  • 2 is the only even prime number.

Worked Examples

Example 1

Listing Factors

Question

List all the factors of 36.

  1. Find pairs that multiply to 36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6.
  2. Write each number once in order.

✓ Answer 1, 2, 3, 4, 6, 9, 12, 18, 36

Example 2

Is It Prime?

Question

Is 91 prime?

  1. Try small primes. 91 is not divisible by 2, 3 or 5.
  2. Try 7: 7 × 13 = 91.
  3. So 91 has factors other than 1 and 91.

✓ Answer No, 91 = 7 × 13

Example 3

Common Multiples

Question

Write the first three common multiples of 4 and 6.

  1. Multiples of 4: 4, 8, 12, 16, 20, 24, ...
  2. Multiples of 6: 6, 12, 18, 24, ...
  3. Numbers in both lists: 12, 24, 36.

✓ Answer 12, 24 and 36

Common Mistakes to Avoid

  • Calling 1 a prime number.
  • Thinking all odd numbers are prime. For example, 9 and 15 are odd but not prime.
  • Forgetting 1 and the number itself when listing factors.
  • Mixing up factors and multiples: factors are smaller or equal, multiples are larger or equal.

Practice Questions

0 of 5 answered
Q1Which of these is a factor of 28?
Q2Which is a prime number?
Q3What is the third multiple of 9?
Q4How many factors does 20 have?
Q5Is 57 prime?

Frequently Asked Questions

Is 2 a prime number?

Yes. It has exactly two factors, 1 and 2, and it is the only even prime.

How can I test whether a big number is prime?

Check divisibility by each prime up to the square root of the number. If none divide it exactly, it is prime.

Take This Guide With You

Get a free printable PDF with the worked examples and quiz answers. Enter your email and the download starts straight away.

Sources and Review

Reviewed by StudyMorrow editorial review on 5 Nov 2026.