Prime Numbers, Factors and Multiples Explained for Kids

By the Success Tutoring team · October 5, 2026

Factors, multiples and prime numbers are where times tables start to get interesting. Children who know their tables well can explore how numbers are built, spot patterns and solve puzzles. The words are easy to mix up, though, so this guide explains each one simply, with examples you can try at the kitchen table.

The key words

A simple way to remember the difference: factors are few, multiples are many. A number has a limited set of factors, all no bigger than itself, but its multiples go on forever.

Step 1: Build factors with arrays

Give your child 12 counters and ask how many different rectangles they can make. They will find 1 row of 12, 2 rows of 6 and 3 rows of 4 (plus the same rectangles turned around). The side lengths are the factors: 1, 2, 3, 4, 6 and 12.

Now try 7 counters. The only rectangle is a single row of 7. That's what makes 7 a prime number: it can't be arranged into any other rectangle.

Step 2: Find factors in pairs

Factors come in pairs that multiply together. Work upwards from 1 so none are missed. For 36:

• 1 × 36
• 2 × 18
• 3 × 12
• 4 × 9
• 5 doesn't divide 36 exactly, so skip it
• 6 × 6, and the pairs have met in the middle, so stop

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36. Writing them as a “rainbow”, with arcs joining each pair, is a nice visual check. The factors worksheet gives lots of practice.

Step 3: Prime and composite numbers

A prime number has exactly two different factors: 1 and itself. The prime numbers below 50 are:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

A composite number has more than two factors, such as 9 (1, 3, 9) or 15 (1, 3, 5, 15). Some facts children enjoy:

• 2 is the only even prime. Every other even number can be divided by 2.
• Not every odd number is prime. 9, 15, 21, 25 and 27 are all composite.
• 91 is a famous trick question. It looks prime but it's 7 × 13.

Try the prime and composite numbers worksheet to sort numbers into each group.

Why 1 is not a prime number

This is the question every class asks. A prime has exactly two different factors, and 1 only has one factor (itself), so it doesn't qualify. There's a deeper reason too. Every whole number greater than 1 can be written as a product of primes in exactly one way, such as 12 = 2 × 2 × 3. If 1 counted as prime, you could write 12 = 1 × 2 × 2 × 3 or 1 × 1 × 2 × 2 × 3, and that neat rule would break. So 1 is neither prime nor composite: it's in a group of its own.

Find primes with the Sieve of Eratosthenes

This 2,000-year-old method is a lovely hands-on activity with a printed 100 square:

1. Cross out 1.
2. Circle 2, then cross out all the other multiples of 2 (4, 6, 8…).
3. Circle 3, then cross out all the other multiples of 3 (6, 9, 12…).
4. Do the same for 5 and 7.
5. Every number left is prime. There are 25 primes up to 100.

You can stop after 7 because 11 × 11 = 121, which is already past 100. Any composite number up to 100 must have a factor of 7 or less.

Divisibility rules that help

Factor trees and prime factors

Older children can break a number down into primes with a factor tree. Split 60 into any factor pair, such as 6 × 10, then keep splitting until every branch ends in a prime: 6 = 2 × 3 and 10 = 2 × 5. So 60 = 2 × 2 × 3 × 5. Whichever pair you start with, you always end up with the same primes.

Common factors and common multiples

• Highest common factor (HCF), also called the greatest common factor (GCF): the biggest number that divides into both. The factors of 12 are 1, 2, 3, 4, 6, 12 and the factors of 18 are 1, 2, 3, 6, 9, 18, so the HCF is 6.
• Lowest common multiple (LCM), also called the least common multiple: the smallest number in both times tables. For 4 and 6, the LCM is 12.

A real-life puzzle: sausages come in packs of 6 and bread rolls in packs of 8. What's the smallest number of each you can buy so none are left over? The LCM of 6 and 8 is 24, so buy 4 packs of sausages and 3 packs of rolls.

Common mistakes

• Mixing up factors and multiples. Remember: factors fit into a number; multiples come out of its times table.
• Missing factor pairs. Work through 1, 2, 3… in order and stop when the pairs meet.
• Thinking 1 is prime, or that 2 can't be prime because it's even.
• Assuming odd means prime. Check 9, 21, 51, 57 (3 × 19) and 91.

When do children learn about primes and factors?

Children usually explore factors and multiples around Grade 4 to Grade 5, and prime and composite numbers around Grade 5 to Grade 6. Strong times tables make all of this much easier, so keep practising with the Times Tables Challenge. Square numbers have a special pattern of factors too, which our guide to square and cube numbers explains.

Frequently asked questions