Prime Factor Decomposition

Factors are things that are multiplied together
Prime numbers are numbers which have exactly two factors
- Themselves and 1
The prime factors of a number are therefore all the prime numbers which multiply to give that number
You should remember the first few prime numbers:
- 2, 3, 5, 7, 11, 13, 17, 19, …

Use a FACTOR TREE to find prime factors
- Split a number up into a pair of factors which multiply to give the number
- Continue splitting up numbers until you get to a prime number
  - These can not be split into anything other than 1 and themselves
A number can be uniquely written as a product of prime factors
- Write the prime factors IN ASCENDING ORDER with × between
  - e.g. 72 = 2 × 2 × 2 × 3 × 3
- Write with POWERS if asked
  - e.g. 72 = 2³ × 3²

This is one of those topics where questions can use different phrases that all mean the same thing …

Find the prime factors of 360.

Give your answer in the form $2^{p} \times 3^{q} \times 5^{r}$ , where $p$ , $q$ and $r$ are integers to be found.

For each number find any two numbers, (not 1), which are factors and write those as the next pair of numbers in the tree.

If a number is prime, put a circle around it.

When all the end numbers are circled, you are done!

Factor-Tree-360, IGCSE & GCSE Maths revision notes

Write down all of the circled numbers, don't miss any of the repeated ones.

For any numbers that are repeated, write them as powers of the number.

$360 = 2 \times 2 \times 2 \times 3 \times 3 \times 5$

You don't usually have to write a "1" as a power if there is a number that isn't repeated, but in this question, it has asked for it.

$360 = 2^{3} \times 3^{2} \times 5^{1}$

Prime Factor Decomposition (CIE IGCSE Maths: Core)