# 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

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