How do I find the prime factors of a number?

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The most common way of doing this is called a bubble search (this may not be the technical name, but it's the one I was taught). The method is as follows:

Start by writing the number at the top of your page. Now find 2 numbers which multiply to that number (e.g. starting with 100, I might find 2 and 50). Draw lines down from 100 to the numbers 2 and 50. Check whether or not these numbers are primes (e.g. check whether 2 and 50 are primes - 2 is, 50 isn't). If you have found a prime number, draw a bubble around it. Now do the same process for 50. I find the factors 2 and 25. 2 is prime, 25 isn't. I draw a bubble around 2 and start again from 25. I find the numbers 5 and 5. both are prime so I bubble both.

Now that I've circled both numbers, my search is complete: the prime factors are the numbers in bubbles.

Note that, if neither number is prime, you have to apply the method to both numbers. Because of this, it's often best to find a prime number for one of the 2 numbers.

Some tricks to make this easier are:

If the number is even, use 2 as one of your factors.

If the number ends with a 5 or a 0, use 5 as one of your factors.

If the digits of the number add up to a multiple of 3, use 3 as one of your factors.

Seb G. 11 Plus Maths tutor, 13 plus  Maths tutor, A Level Maths tutor...

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