How do you find the prime factorisation of a large number like 420?

You start by dividing 420 by whichever numbers you know that it is divisible by.

420 is obviously divisible by 10 so you can start with 10 x 42.

Then, you factorise 10 and 10 = 2 x 5, so now we know 420 = 2 x 5 x 42.

42 is an even number, so we can divide by 2. 2 x 5 x 2 x 21. 21 = 3 x 7.

Therefore:

420 = 2 x 5 x 2 x 3 x 7.

As 2, 3, 5 and 7 are all prime numbers the factorisation is almost complete. However, as we have 2 x 2, this is factorised as 2^2.

Then, we write the primes out in numerical order, starting with powers:

420 = 2^2 x 3 x 5 x 7.

AA
Answered by Abisayo A. Maths tutor

3092 Views

See similar Maths 11 Plus tutors

Related Maths 11 Plus answers

All answers ▸

How do I work out the area of a right angled triangle?


A sunflower is one hundred and fifty centimetres tall. How tall will it be if its height increases by ten per cent?


What is the value of the figure 1 in the number 2105?


When a fifth of the class is absent, there are 24 pupils present. What is the total number of pupils in the class?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning