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What Is a Prime Number?

In one line: A prime number is a whole number bigger than 1 that has exactly two factors: 1 and itself. A factor is a whole number that divides into another number with nothing left over.

Why it works

Prime numbers are the building blocks of all whole numbers. Every whole number bigger than 1 is either prime or can be made by multiplying primes together, like 12 = 2 × 2 × 3. Numbers that are not prime (and bigger than 1) are called composite numbers. Knowing primes makes it easier to simplify fractions, find common factors and spot number patterns. Primes are also used in real life to keep online messages and bank details secret.

Think of it like: Imagine you have some square tiles and you want to arrange all of them into a neat rectangle. With 12 tiles you have lots of choices: 1 row of 12, 2 rows of 6, or 3 rows of 4. But with 7 tiles, the only rectangle you can make is one long row of 7 (or 7 rows of 1, which is the same shape turned around). Numbers like 7 that can only make one long thin row are prime. (Where this breaks: The tile picture breaks down for the number 1: one tile also makes only one row, but 1 is not a prime number because it has only one factor (itself), not two. The analogy also gets slow for big numbers, where it is quicker to test by dividing than by drawing tiles.)

Worked example

Is 51 a prime number?

  1. Check 2: 51 is odd, so 2 is not a factor.
  2. Check 3: add the digits, 5 + 1 = 6. Since 6 can be divided by 3, so can 51.
  3. Divide to be sure: 51 ÷ 3 = 17, with nothing left over.
  4. So 51 = 3 × 17. It has factors 1, 3, 17 and 51, which is more than two factors.

Answer: 51 is not prime. It is a composite number because 51 = 3 × 17.

Common mistakes

  • Thinking 1 is prime: fix this by remembering a prime needs exactly two different factors, and 1 has only one factor.
  • Thinking every odd number is prime: test odd numbers like 9, 15, 21 and 51 by dividing, because all of them have other factors.
  • Thinking 2 cannot be prime because it is even: 2 has exactly two factors (1 and 2), so it is prime, and it is the only even prime.
  • Giving up the checks too early, for example calling 91 prime: keep testing primes like 7 and 11, because 91 = 7 × 13.

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Questions parents ask

What year do kids learn about prime numbers?

In the UK, children meet prime numbers in Year 5 and use them more in Year 6. In Australia they are a focus in Year 6, and in the US children learn to tell prime from composite numbers in Grade 4.

Why is 1 not a prime number?

A prime number must have exactly two different factors, and 1 has only one factor: itself. Mathematicians also leave 1 out so that every whole number can be broken into primes in just one way.

How can I help my child learn prime numbers at home?

Give your child a handful of counters or coins and ask them to make rectangles: if only one long row works, the number is prime. You can also colour a 1 to 100 grid together, crossing out multiples of 2, 3, 5 and 7 to reveal the primes.

Does my child need to memorise prime numbers?

It helps to know the primes up to 20 by heart (2, 3, 5, 7, 11, 13, 17, 19), and many children learn them up to 50 or 100 by about age 11. More important than memorising is knowing how to test a number by dividing.