Factors and multiples — for parents
Year 4 is where children meet factors and multiples as named concepts (CCSS 4.OA.B.4, NC Year 4). They've been using them every time they did a times table; this year the vocabulary gets nailed down, and primes show up for the first time.
What your child should master by year-end
- List all factors of a number up to ~50.
- List the first several multiples of a number.
- Decide whether a number ≤ 50 is prime (exactly two factors) or composite (more than two factors).
- Find a common multiple of two small numbers.
- Use the divisibility tricks for 2, 3, 5 and 10.
Common mistakes
Mixing up "factor" and "multiple"
Children often muddle the two words. Useful phrasing:
- A factor is a number that fits inside another (it divides it).
- A multiple is what another number turns into when multiplied.
So 4 is a factor of 12, and 12 is a multiple of 4. Same relationship, two different ends.
Help: practise saying both sentences after each example. "3 is a factor of 12. 12 is a multiple of 3."Missing a factor
When listing factors, children sometimes skip a pair — e.g. listing 1, 2, 4, 6, 12 for the number 24 but forgetting 3 and 8.
Help: encourage a systematic approach. Try 1, 2, 3, 4, … in order until the next factor's pair is smaller than what you've already tested. Keep them written down as pairs (1 × 24, 2 × 12, …).Thinking 1 is prime
It's a natural guess, but 1 is not a prime. The definition requires exactly two distinct factors. 1 has only one.
Help: stick to the strict count. "A prime has exactly two factors. 1 has only one. So 1 isn't a prime."Treating 2 as composite
Some children look at 2 and think "even, so composite". But 2 has only two factors (1 and 2), so it's prime.
Help: remind them that "even" just means divisible by 2 — it doesn't say anything about how many factors there are.Things to try at home
Arrange objects in rectangles
Give your child a number of coins or pebbles and ask them to arrange them in a rectangle. How many different rectangles work?
- 12 coins: 1×12, 2×6, 3×4. Three rectangles → six factors.
- 7 coins: only 1×7. One rectangle → two factors → prime.
You can see at a glance whether a number is prime: if the only rectangle is a single row, it's prime.
Times-table grid
Pull up or print a 12×12 multiplication grid. The numbers that appear are composite (with at least two factors each). The numbers that don't appear between 2 and 12 (just 2, 3, 5, 7, 11) are prime.
Shared bus problem
"Bus A leaves every 6 minutes. Bus B leaves every 8 minutes. They both leave at 9:00. When do they leave together again?" — list the multiples of 6 and 8 until you find one in common. (24 minutes later, 9:24.)