Question

What is the unit digit of 1!+2!+3!.........19921823!

Answer 1

Let's see if there's anything useful.

• 1!=1

• 2!=2(multiply 2 to 1!)

• 3!=6(multiply 3 to 2!)

• 4!=24(multiply 4 to 3!)

• 5!=120(multiply 5 to 4!)

• And so on...

First, 5! gets 0 for the first because there are 2 and 5 as factors. The rules will go on. If we multiply any number to 5! it will have at least one zero.

Therefore, the unit digit will be 1+2+6+4=13. Since we count unit digit the answer is three.