Factors of a number are the integers (whole numbers) that divide into it without any remainders or decimals.

Factors can also be thought of as the times tables in which a number appears.

Every number have a finite amount of factors (numbers with exactly two factors are called the prime numbers).

For example:

The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

The prime factors of a number are the factors which are also prime numbers. In the case of 36, 2 and 3 are its prime factors.

To write 36 as a product of its prime factors, we need a combination of 2 and 3 that we can multiply together to make 36. In this case it’s:

2 x 2 x 3 x 3

Try it. Guarantee it will make 36.

Every number can be written as a unique combination of prime numbers. Prime numbers are like the atoms, the indivisible building blocks, of numbers.

A common method for figuring out what combination of prime numbers you need, is to use something called a factor tree (sometimes referred to as prime factor decomposition).

Factor Tree

This is best where you start at the top and split your number off into factors as shown:

Factor Tree

Each time you get a prime you circle it and you finally end up with all the prime factors, which you can arrange in order.

420 = 2 x 2 x 3 x 5 x 7

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Unit 2 June 2011 (F) Page 8, Question 13

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