Express 300 as a product of its prime factors.

Factors of a number are: numbers that can be multiplied (by a whole number/ integer) to make the original number. For example, 6 is a factor of 42, because 6 can be multiplied by 7 to make 42.

Prime numbers are numbers that cannot be divided by anything except themselves and 1 to give a whole number answer; for example 3 and 11.

Each time you find a prime factor, circle it in your working, so you do not end up missing one out in your final answer - in this example I underline each prime factor I find.

In order to split 300 into its prime factors, first of all think of a number than goes into 300:

-Let us start with 30. 30 goes into 300 at total of 10 times, as 30x10=300.

-So, we now have two factors of 300: 30 and 10. Now, we must find the factors of these two numbers:

- Factors of 10: 5 x 2 = 10. As the numbers 5 and 2 are both prime numbers, they are counted as prime factors for 300.

-Factors of 30: 3 x 10 = 30. As 3 is a prime number, we have found another prime factor of 300.

However, 10 is not a prime factor, and so we must keep going: 5 x 2 = 10, and therefore we have found another two prime factors: 5 and 2.

Looking back over your working, write down every number that is circled (or in this case, underlined): 5, 2, 3, 5, 2

So, we can write 300 as a product (multiplication) of its prime factors by multiplying them all: 2 x 2 x 3 x 5 x 5

This can be rewritten as 22 x 3 x 52

Answered by Alice M. Maths tutor

63850 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Ben wants to book tickets to see a concert. The price of the ticket is £65. He must also pay a booking fee, which is 15% of the ticket price. Ben has £75, does he have enough money to pay for the ticket and booking fee?


Before an exam, I always go through as many past papers as possible but I still don't know how to do the questions on an exam when they come up, why and what can I do?


There are only red , blue and purple counters in a bag. The ratio of the number of red counters to the number of blue counters is 3 : 17. If a counter is taken randomly the probability that it is purple is 0.2 Work out the probability for it to be red.


A car costs £1200 in a sale. It was reduced by 20%. What was the original price?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy