Step by step
The question
Question: find the prime factors of 360.
A prime number has exactly two factors: 1 and itself.
Like 2, 3, 5, 7 and 11.
We want 360 as primes multiplied together.
1 Make a factor tree
We start with 360 at the top.
We split 360 into two numbers that multiply to make it.
Any pair works.
360 is 18 times 20.
18 is 3 times 6.
3 is prime.
We circle it: a prime can't be split.
6 is 2 times 3.
2 and 3 are both prime.
20 is 4 times 5.
5 is prime.
4 is 2 times 2.
2 and 2 are both prime.
2 Collect the primes
We collect the circled numbers, smallest first.
2 shows up 3 times.
So 2 times 2 times 2 is written 2 cubed.
3 shows up 2 times.
So 3 times 3 is written 3 squared.
3 Check
Let's check: we multiply them back.
2 times 2 is 4.
4 times 2 is 8.
8 times 3 is 24.
24 times 3 is 72.
72 times 5 is 360.
We get 360 again.
So it is right!
Let's look back.
First: make a factor tree.
Then: collect the primes.
Last: check.