Step by step
The question
Question: work out 5 factorial.
5! =
1 Write it out
5 factorial means 5 times every whole number below it, down to 1.
5! = 5 × 4 × 3 × 2 × 1
Factorial: multiply down to 1.
n! = n × (n − 1) × … × 1
Careful!
Factorial means times, not plus.
Careful: not 5 + 4 + 3 + 2 + 1 = 15 ✗
2 Multiply
5 times 4 is 20.
20 times 3 is 60.
60 times 2 is 120.
Times 1 changes nothing.
5 × 4 = 20
20 × 3 = 60
60 × 2 = 120
So 5 factorial is 120.
5! = 120
3 Check
Let's check the other way round: 1 times 2 is 2, then 6, then 24, then 120.
The same.
So the answer is right!
1 × 2 × 3 × 4 × 5: 2, 6, 24, 120 ✓
Let's look back.
First: write it out.
Then: multiply.
Last: check.
Answer
5! = 120