Step by step
The question
Question: find the prime factors of 72.
Prime factors of 72
A prime number has exactly two factors: 1 and itself.
Like 2, 3, 5, 7 and 11.
We want 72 as primes multiplied together.
prime: only 1 × itself
2, 3, 5, 7, 11, 13, ...
1 Make a factor tree
2 Collect the primes
We collect the circled numbers, smallest first.
= 72 = 2 × 2 × 2 × 3 × 3
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.
= 72 = 23 × 32
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.
2 × 2 = 4, 4 × 2 = 8
8 × 3 = 24, 24 × 3 = 72
We get 72 again.
So it is right!
Let's look back.
First: make a factor tree.
Then: collect the primes.
Last: check.
Answer
= 72 = 23 × 32