Step by step
The question
Question: work out 6 factorial.
6! =
1 Write it out
6 factorial means 6 times every whole number below it, down to 1.
6! = 6 × 5 × 4 × 3 × 2 × 1
Factorial: multiply down to 1.
n! = n × (n − 1) × … × 1
Careful!
Factorial means times, not plus.
Careful: not 6 + 5 + 4 + 3 + 2 + 1 = 21 ✗
2 Multiply
6 times 5 is 30.
30 times 4 is 120.
120 times 3 is 360.
360 times 2 is 720.
Times 1 changes nothing.
6 × 5 = 30
30 × 4 = 120
120 × 3 = 360
360 × 2 = 720
So 6 factorial is 720.
6! = 720
3 Check
Let's check the other way round: 1 times 2 is 2, then 6, then 24, then 120, then 720.
The same.
So the answer is right!
1 × 2 × 3 × 4 × 5 × 6: 2, 6, 24, 120, 720 ✓
Let's look back.
First: write it out.
Then: multiply.
Last: check.
Answer
6! = 720