How do I find the prime factors of a number?

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...

6 months ago

Answered by Seb, a 11 Plus Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£30 /hr

Cesare Giulio A.

Degree: Mathematics (Doctorate) - Manchester University

Subjects offered:Maths, Further Mathematics

Further Mathematics

“I come from Italy, where I have been a tutor for 8 years, helping more than 100 students in Mathematics and Physics. ”

MyTutor guarantee

£18 /hr

Abisayo A.

Degree: PgDip Cognitive Behaviour Therapy (Other) - Birmingham University

Subjects offered:Maths, Religious Studies+ 1 more

Religious Studies

“Hello there! My name is Abisayo Abisayo (Abz) and I am currently studying a part-time postgraduate diploma in Cognitive Behavioural Therapy, and working part time as a Special Educational Needs Teaching Assistant in Birmingham. I am r...”

MyTutor guarantee

£20 /hr

Ben C.

Degree: English Literature (Bachelors) - Durham University

Subjects offered:Maths, Spanish+ 4 more

English Literature
English Language

“About me Hello! I am an English student at Durham University. English has always been my favourite subject, and choosing to do it at university was a very easy decision for me. So, if you’re looking for English tuition then I’m your m...”

About the author

£18 /hr

Seb G.

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths


“Me: I'm a second year maths student at the University of Bath. I fell in love with maths after a rocky start with the subject, so believe that I can help people regardless of whether they like maths or not.  I've been tutoring maths l...”

MyTutor guarantee

You may also like...

Posts by Seb

How do I differentiate implicitly?

How do I evaluate composite functions?

How do I find the prime factors of a number?

How do I multiply decimal numbers?

Other 11 Plus Maths questions

When a price changes from £15 to £20. By how much percentage has the price changed?

Sunita has 75 pens and she ties them into bundles of 8. How many pens does she have left over?

How many thirds are there in 9?

If Lisa loses 23% of £650, how much has she lost?

View 11 Plus Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss