Multiples, Factors and Prime Factors

The MULTIPLES of a number are what you get when you multiply that number by an integer. To put it more simple, multiples are just a number’s times table.

So the multiples of 8 are 8, 16, 24, 32 etc.

NOTE: Every number is also its own multiple – so you can see above that 8 is a multiple of 8 (it’s just 8 x 1).

The FACTORS of a number are all the numbers that divide into it.

So the factors of 8 are 1, 2, 4, 8.

Also remember that two minus numbers multiplied together make a positive number. So -2 x -4 = 8. This means that the factors of 8 are also -1, -2, -4 and -8.

You might be asked about the highest common factors and lowest common multiples of numbers in the exam which we also have a revision pageĀ on.

A PRIME FACTOR of a number is, as you’d expect, a prime number that divides into it. This is important as you could be asked to express a number as a “product of prime factors” and in such a case you can use the factor tree method to find which prime factors multiply together to make the number in the question.

Example: Express 42 as a product of prime factors.

42-factor-tree (1)

So here’s how you do it:

  • Start by writing the number at the top of the tree.
  • Split it out into two factors (any you like, here we chose 2 and 21, but we could have chosen 6 and 7)
  • Keep splitting each number until you come to a prime number
  • The answer is the prime numbers you find multiplied together

ANSWER: 42 = 2 x 3 x 7

Right now you’re probably thinking “When would this ever be useful!”. Well, finding prime numbers is incredibly important to cryptography – the study of code braking and in fact prime factorisation played a huge part in the code breaking efforts of Alan Turing in the Second World War. So maths can be cool right? *coughs*

example questions

What are the first 5 multiple of 4?
4, 8, 12, 16, 20. Easy!

What are the factors of 24?
1, 2, 3, 4, 6, 8, 12, 24. Simple as that.
Expres s40 as a product of prime factors
2 x 2 x 2 x 5. Rememer that ‘product’ just means multiplying things together. Hopefully you used the factor tree method above.
Express 126 as a product of prime factors
2 x 3 x 3 x 7. This one is a bit harder, but stick to the factorisation tree method and you can answer any question like this. You got this!