Factors are numbers that you multiply together to get another number – they are always whole numbers and not fractions.
For example the factors of 24 are 1 and 24, 2 and 12, 3 and 8, 4 and 6 (or 1, 2, 3, 4, 6, 8, 12, 24).
Factors are super important in maths – and in the real world. They help us simplify fractions, solve algebraic equations and even encrypt data on the internet.
The most important thing you can do is learn your timestables, but you can also use 4 simple tricks to make it easier (and help you learn to think more mathematically). Also, we only learn up to the 12x table, so knowing our tables isn’t enough for large numbers.
Btw for those that find this too easy, there’s something cool you probably don’t know at the end of this post.
Trick 1: If a number ends in 0, 10 is a factor.
Look at the 10x table: 10, 20, 30, 40, 50, 60……… everything ends in 0.
You can divide any number that ends in 0 by 10.
Trick 2: If a number ends in 0 or 5, 5 is a factor.
Look at the 5x table: 5, 10, 15, 20, 25, 30, 35, 40, 45…. everyting ends in 0 or 5.
You can divide any number that ends in 0 or 5 by 5.
Trick 3: Every even number has 2 as a factor
That’s actually the definition of an even number! So if it’s even, go ahead and divide by 2.
Trick 4: The factors of an odd number are always odd
Why? If an odd number had an even factor, that even factor could be divided by two. That would mean that the odd number could be divided by two, which it can’t be as that would make it an even number.
Don’t worry if you didn’t follow that! All you need to remember is that odd numbers have odd factors, so you don’t have to waste your time trying out the even ones.
Try 3 first, then 7 (we covered 5 in Trick 2), then 11 (if 9 is a factor then 3 is also a factor so we’ve already covered it). If you need to keep going (hopefully not!) then use prime numbers – they don’t have any other numbers as factors. So that’s 13, 17, 19, 23….
So whenever you need to find a factor of a number, ask yourself these questions:
1) Does it end in 0?
2) Does it end in 5?
3) Is it an even number?
4) Can I divide it by 3? Or by 7, 11 or 13?
These aren’t really tricks, they’re things you need to notice to be fluent in the language of maths.
But there are some other tricks you can use if you want to impress your family and friends (who I’m sure think maths is really cool). These are more tricks than basic maths – they’re harder to understand, and you don’t need to know them so only learn them if you want to.
Magic Trick 1: If the digits of a number add up to 3, then 3 is a factor.
Magic Trick 2: If the last two digits of a number are divisible by 4, then 4 is a factor.
This is because 100 is divisible by 4, and so is 1,000, 10,000, 100,000, etc. So if the last two digits are divisible by four and you add hundreds, thousands, etc you’re just adding another number that is divisible by four.