Step by step
The question
Question: work out 7 factorial.
7! =
1 Write it out
7 factorial means 7 times every whole number below it, down to 1.
7! = 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 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28 ✗
2 Multiply
7 times 6 is 42.
42 times 5 is 210.
210 times 4 is 840.
840 times 3 is 2520.
2520 times 2 is 5040.
Times 1 changes nothing.
7 × 6 = 42
42 × 5 = 210
210 × 4 = 840
840 × 3 = 2520
2520 × 2 = 5040
So 7 factorial is 5040.
7! = 5040
3 Check
Let's check the other way round: 1 times 2 is 2, then 6, then 24, then 120, then 720, then 5040.
The same.
So the answer is right!
1 × 2 × 3 × 4 × 5 × 6 × 7: 2, 6, 24, 120, 720, 5040 ✓
Let's look back.
First: write it out.
Then: multiply.
Last: check.
Answer
7! = 5040