Step by step
The question
Question: find the prime factors of 84.
Prime factors of 84
A prime number has exactly two factors: 1 and itself.
Like 2, 3, 5, 7 and 11.
We want 84 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.
= 84 = 2 × 2 × 3 × 7
2 shows up 2 times.
So 2 times 2 is written 2 squared.
= 84 = 22 × 3 × 7
3 Check
Let's check: we multiply them back.
2 times 2 is 4.
4 times 3 is 12.
12 times 7 is 84.
2 × 2 = 4, 4 × 3 = 12
12 × 7 = 84
We get 84 again.
So it is right!
Let's look back.
First: make a factor tree.
Then: collect the primes.
Last: check.
Answer
= 84 = 22 × 3 × 7