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...

4 weeks ago

Answered by Seb, a 11 Plus Maths tutor with MyTutor

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


Shannon W. 13 plus  Maths tutor, 11 Plus Maths tutor, A Level Maths t...
View profile
£18 /hr

Shannon W.

Degree: Chemistry with Medicinal Chemistry (Masters) - Newcastle University

Subjects offered: Maths, Science+ 3 more

-Personal Statements-

“About me: I am a chemistry student at Newcastle University. I have always been interested in science and mathematics, and can sit for hours watching documentaries on the subjects. I really enjoy getting stuck into exam questions and ...”

Alexander C. IB Business Studies tutor, GCSE Business Studies tutor, ...
View profile
£18 /hr

Alexander C.

Degree: Accountancy (Bachelors) - Durham University

Subjects offered: Maths, French+ 5 more

English Literature
English Language
Business Studies
-Personal Statements-

“Hi! My name is Alex, and I am currently a student at Durham University, studying Accountancy! I came to Durham from The Netherlands, having spent my entire life there, but have British and French parents. Having gone to an internation...”

Jayde L. GCSE English tutor, 11 Plus English tutor, IB English tutor,...
View profile
£18 /hr

Jayde L.

Degree: Psychology (Bachelors) - York University

Subjects offered: Maths, Biology


“​About Me: I am currently majoring in BSc Psychology at The University of York. I volunteer at the Nursery and write reviews for one of the University's valued arts magazines. For years, I had spent most of my time in Math classes; w...”

MyTutor guarantee

About the author

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

The average age of a group of 6 people is 21. One more person joins the group and the average is now 25. How old is the new member of the group?

Write 120 as a product of its prime factors.

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

How do you work out 3/5 of 60?

View 11 Plus Maths tutors


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