# Number

Primes

A prime number is a number with special properties. Prime numbers can only be divided into integers (whole numbers) by the number1 and itself. Any whole number that divides exactly into another number is called a factor.

For example: The number 3 is a prime number because 3 ÷ 1 = 3 and 3 ÷3 =1. These are the only two numbers that 3 can be divided by

What about 5,  is it a prime number ?

Ask yourself! What numbers can 5 be divided by so that the answer is a whole number?

The answer is 1 and 5, so 5 is a prime number.

It would seem that all prime numbers must be odd numbers. Do you know why?

Any even number can be divided by 1, itself and the number 2. This means that any even number is not a prime number except the number 2.

1 and 2 can only divide the number 2.

So remember any even number apart from the number 2 is NOT a prime number.

Does this mean that ALL odd numbers are prime?

NO what about the number 9?

The number 9 can be divided by 1, 3, 9 to make whole numbers. So although 9 is odd it is not a prime number.

9 has 3 factors

Which numbers are prime between 1 and 20 (inclusive).

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

Well how did you do?

next

It is easy to find a prime number while they are small numbers, but what about bigger numbers?

Here is a hundred square, see if you can find the primes in this.

 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

 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

The prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101.

You could have got rid of all the even numbers first, then every number that you could divide by 3.
Then every number you could divide by 5 then 7 then 9 then 11.

Well, I hope you didn't find that too hard!

Let me finish with a definition of a prime number:

A prime number is an integer greater than one that as only two positive factors, the number one and itself.

Good luck!