Question

The last non-zero digit in 20! is ___

Answer 1

Find exponent of prime numbers like

2, 3, 5, 7, 11, 13, 17, 19 in 20!

We get 20! = $2^{18}.3^8.5^4.7^2.{11}^1.{13}^1.{17}^1.{19}^1$

$={10}^4(2^{14}.3^8.7^2.{11}^1.{13}^1.{17}^1.{19}^1)$

$\therefore 2^{14}$ ends with 4,

$7^2$ ends with 9,

$3^8$ ends with 1 and product of remaining terms ends with 9.

Hence last non-zero digit in 20! = 4