Step by step
The question
Question: find the prime factors of 252.
A prime number has exactly two factors: 1 and itself.
Like 2, 3, 5, 7 and 11.
We want 252 as primes multiplied together.
1 Make a factor tree
We start with 252 at the top.
We split 252 into two numbers that multiply to make it.
Any pair works.
252 is 14 times 18.
14 is 2 times 7.
2 and 7 are both prime.
We circle them: a prime can't be split.
18 is 3 times 6.
3 is prime.
6 is 2 times 3.
2 and 3 are both prime.
2 Collect the primes
We collect the circled numbers, smallest first.
2 shows up 2 times.
So 2 times 2 is written 2 squared.
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 3 is 12.
12 times 3 is 36.
36 times 7 is 252.
We get 252 again.
So it is right!
Let's look back.
First: make a factor tree.
Then: collect the primes.
Last: check.