Step by step
The question
Question: find the prime factors of 250.
Prime factors of 250
A prime number has exactly two factors: 1 and itself.
Like 2, 3, 5, 7 and 11.
We want 250 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.
= 250 = 2 × 5 × 5 × 5
5 shows up 3 times.
So 5 times 5 times 5 is written 5 cubed.
= 250 = 2 × 53
3 Check
Let's check: we multiply them back.
2 times 5 is 10.
10 times 5 is 50.
50 times 5 is 250.
2 × 5 = 10, 10 × 5 = 50
50 × 5 = 250
We get 250 again.
So it is right!
Let's look back.
First: make a factor tree.
Then: collect the primes.
Last: check.
Answer
= 250 = 2 × 53