How do you find the prime factors of a number?

Sebastian, to find the prime factors of a number you can use the following method which is famously known as tree diagram!

Shaeera’s answer is great but I hope you both doesn’t mind me adding some additional tips and tricks.

You probably already know a number ending in 5 or 0 is divisible by 5

You probably also know that a number ending in an even number is divisible by 2.

Putting those facts together, if I need to prime factorise a number I check

1) Is it even

2) Is it divisible by 5

Then start on the factor tree.

For non obvious factors I’ve used the following ‘tricks’

A number divisible by 3 has the sum of its digits divisible by 3.

eg 138 is divisible by 3 because 1+3+8=12. That’s a multiple of 3. Using short division you’ll see that it’s 46x3.

The same goes for 195. 1+9+5 =15= a multiple of 3. You can check that 3 goes into 195 yourself with short division or a calculator.

Exactly the same ‘trick’ works for multiples of 9.

Take 6786 and add up the digits. I think you’ll get 27, a multiple of 9.

6786 divided by 9 is 754.

Last (particularly neat trick). Unfortunately it only works on 3 digit numbers when the outside digits add up to less than 10.

682= 62x11

792= 72x11

583=53x11

Take a 3 digit number, add the outer digits and if they equal middle digit, you have the outer digits.

My advice is

1) look for factors you know

2) look for things like 3, 9 and 11as factors.

3) draw Shaeera’s diagram and work like she has

All the above is great, just thought I'd add another angle - it still requires Ros's tricks and tips :o)