Year 9 maths lesson · Factors, Multiples, Primes

Factors, Multiples and Primes

Learn what factors, multiples, and prime numbers are, and how they relate to each other. Understand factor pairs, why 1 is not prime, and the key distinction — factors divide in (smaller), multiples multiply out (bigger).

  • About 4–7 minutes
  • 10 quick questions as you go
  • Then about 5 minutes of practice
Practice questions → Set for Class

Worked examples

Finding all factors of 12 using factor pairs

  1. List pairs that multiply to 12: 1 × 12, 2 × 6, 3 × 4
  2. Factors of 12: 1, 2, 3, 4, 6, 12
  3. Factor pairs ensure you don’t miss any

Why 1 is not a prime number

  1. A prime must have exactly 2 distinct factors
  2. 1 only has one factor — itself
  3. So the first five primes are 2, 3, 5, 7, 11
  4. 2 is the only even prime (every other even number is divisible by 2)

Factors vs multiples — the key distinction

  1. Multiples of 5 are the 5 times table: 5, 10, 15, 20, …
  2. 3 is a factor of 12 (3 fits inside 12)
  3. 12 is a multiple of 3 (12 is built from 3s)
  4. Factors divide IN (get smaller), multiples multiply OUT (get bigger)

Before this lesson

It helps to be comfortable with:

  • Multiplication and division facts

Lesson transcript

Everything the lesson says, word for word

Student: Hey Alex! What are we looking at today?

Teacher: Factors, multiples, and primes.

Student: Oh easy, I know all this from last year.

Teacher: Go on then, what's a factor?

Student: A factor is a number that goes into another number evenly. Like the factors of 12 are 1, 2, 3, 4, 6, and 12.

Teacher: Good. And they come in pairs — 1 and 12, 2 and 6, 3 and 4. That's how you find them all without missing any.

Teacher: Now primes. What's a prime number?

Student: Hmmm...

Student: A prime number is only divisible by 1 and itself. Like 7 — its only factors are 1 and 7.

Teacher: Good. List me the first five primes.

Student: 1, 2, 3, 5, 7.

Teacher: Close, but 1 isn't a prime. A prime number has to have exactly two distinct factors. 1 only has one factor — itself. So the first five are 2, 3, 5, 7, 11.

Student: And 2 is the only even prime, yeah?

Teacher: Exactly. Every other even number is divisible by 2, so they can't be prime.

Teacher: And what about multiples?

Student: I always get factors and multiples mixed up...

Teacher: Multiples are just the times tables. Multiples of 5 are 5, 10, 15, 20, and so on. It's just the 5 times table.

Teacher: Easy way to remember — factors fit inside a number, multiples get bigger. 3 is a factor of 12, and 12 is a multiple of 3. Same relationship, different direction.

Student: Oh, that makes sense actually.

Teacher: Right, try these questions then.

More Factors, Multiples, Primes lessons

  • Prime FactorisationBreak numbers down into their prime factors and use factorisations to find all factors.
  • HCF and LCMUse prime factorisations and Venn diagrams to find the highest common factor and lowest common multiple.

Next lesson: Prime Factorisation →All Year 9 Number lessonsAll lessons