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Prime numbers

You have most likely heard the term factor before. A factor is a number that goes into another. The factors of 10 for example are 1, 2, 5 and 10.

Prime numbers are a special set of numbers that only have two factors: themselves and 1.

An example of a prime number is 13 as it only has two factors: 13 and 1, whereas 9 is not a prime number as it has three factors: 9, 3 and 1.

The first 10 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

It is interesting to note that 2 is the only even prime number. The number 1 is not prime as it only has a single factor (1 itself), and as we previously mentioned prime numbers must have two factors exactly.

Expressing numbers in prime factor form

Every whole number (with only one exception – the number 1) can be expressed as a product of prime numbers.

Examples

8 = 2 × 2 × 2 = 2³

9 = 3 × 3 = 3²

10 = 2 × 5

39 = 3 × 13

Example

Express 300 in prime factor form.

First we start with the lowest prime number, 2. Because 2 is a factor of 300, we make a note of the '2' and then divide 300 by 2, leaving 150.

We can use a table to make this easier to see:

Now we can divide by 2 again, leaving 75:

We can no longer divide by 2, as 2 is not a factor of 75. We now try to divide by the next largest prime number which is 3:

We can no longer divide by 3, as 3 is not a factor of 25. We must again look for a larger prime number to use. The next prime number in the list is 5:

Finally we can divide by 5 again, leaving 1:

When we have a 1 in the left-hand column, we have finished the process.

From the table we can see that 300 = 2 × 2 × 3 × 5 × 5 = 2² × 3 × 5². You can check this by doing the multiplication on a calculator.