Question

what is the last digit in the product of 1×2×3×4ו•••••••••••••••••×100​

Answer 1

$99 \: \: is \: \: the \: \: last \: \: digit \: \: in \\ the \: \: product$

Answer 2

The Unit’s digit of 10!, 11!, 12!, 13!, 14!, etc. is always 0.

Hence, it would be enough to find the sum of unit’s digit from 1 to 9.

Again, unit’s digit of from 9! to 5!, is zero.

Therefore, the unit’s digit of 4! + 3! + 2! + 1! = (4+ 6 + 2 + 1) = 13; then unit’s digit is 3.

The unit’s digit of 1! + 2! + 3! + …….. 100! = 3.

(If 0! is also added, the unit’s digit would be 3+1=4).