Step by step
The question
Question: work out 8 factorial.
8! =
1 Write it out
8 factorial means 8 times every whole number below it, down to 1.
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
Factorial: multiply down to 1.
n! = n × (n − 1) × … × 1
Careful!
Factorial means times, not plus.
Careful: not 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 36 ✗
2 Multiply
8 times 7 is 56.
56 times 6 is 336.
336 times 5 is 1680.
1680 times 4 is 6720.
6720 times 3 is 20160.
20160 times 2 is 40320.
Times 1 changes nothing.
8 × 7 = 56
56 × 6 = 336
336 × 5 = 1680
1680 × 4 = 6720
6720 × 3 = 20160
20160 × 2 = 40320
So 8 factorial is 40320.
8! = 40320
3 Check
Let's check the other way round: 1 times 2 is 2, then 6, then 24, then 120, then 720, then 5040, then 40320.
The same.
So the answer is right!
1 × 2 × 3 × 4 × 5 × 6 × 7 × 8: 2, 6, 24, 120, 720, 5040, 40320 ✓
Let's look back.
First: write it out.
Then: multiply.
Last: check.
Answer
8! = 40320