## What is a prime number?

Prime numbers are positive

whole numbersthat only havetwo factors, themselves and 1.

This means that** prime numbers **can *only* be made by** multiplying themselves by one** and are *only*** divisible by themselves or one.**

Except the number 2, all prime numbers are odd, but not all odd numbers are prime numbers.

**For example:**

Is 3 is a prime number? Yes.

3 has **only two factors**: 3 and 1. 3 can only be made by multiplying 3 × 1 and is only divisible by itself and 1.

Is 7 a prime number? Yes.

7 has **only two factors**: 7 and 1. 7 can only be made by multiplying 7 × 1 and is only divisible by itself and 1.

Is 9 a prime number? No.

9 has **three factors**: 9, 3 and 1. 9 can be made by multiplying 9 × 1 and 3 × 3 and is divisible by 9, 3 and 1.

Is 1 a prime number? No.

1 is **not a prime number** as it has **only one factor**. 1 is considered a **natural number**.

Here is a really useful and short video to help children understand the concept of prime numbers:

## First 10 prime numbers

The first 10 prime numbers are:

2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 |

## Prime numbers up to 100

There are 25 prime numbers under 100.

Below is a grid of all prime numbers under 100:

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |

51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |

61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |

71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |

81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |

91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |

## How can I check if a number is a prime number?

As children should know their times tables (up to 12 × 12) by the end of Year 4, they should also recognise numbers that don’t appear within those times tables. These are all **prime numbers**.

If children are unsure then the following **prime number testing strategy** may help:

- Check if the number is odd (all prime numbers except 2 are odd).
- Check if the number is a multiple of 5. If it ends with 5 or 0 it is
**not**a prime number (*apart from 5 itself*). - Does the sum of the digits make a multiple of 3? If the sum of the digits is a multiple of three, it is
**not**a prime number. e.g. 87 = 8 + 7 = 15.

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### More commonly asked questions about prime numbers

Is 2 a prime number? Yes.

2 has **only two factors**: 2 and 1. 2 can only be made by multiplying 2 × 1 and is only divisible by itself and 1. Note: 2 is the first and only even prime number.

Is 5 a prime number? Yes.

5 has **only two factors**: 5 and 1. 5 can only be made by multiplying 5 × 1 and is only divisible by itself and 1. Note, 5 is the only multiple of 5 that is a prime number.

### Key Points

- Prime numbers are whole numbers with
**only two factors**, themselves and 1. **1 is not a prime number**as it**only has one factor**.**2 is a prime number**, it is the only even prime number.- 5 is the only multiple of 5 that is a prime number.
- The
**first 10 prime numbers**are: 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. - The
**prime numbers to 20**are: 2, 3, 5, 7, 11, 13, 17 and 19.