Factorial

0! = 1; 1! = 1; 2! = 2; 3! = 6; 4! = 24; 5! = 120; 6! = 720; 7! = 5040 

Trick 1: Rightmost non-zero digit of n! or R(n!)

R(n!) = Last Digit of [ 2^a x R(a!) x R(b!) ]

where n = 5a + b

e.g.

What is the rightmost non-zero digit of 37! ?

 R (37!) = Last Digit of [ 2⁷ x R (7!) x R (2!) ]

 R (37!) = Last Digit of [ 8 x 4 x 2 ] = 4

Trick 2: Power of a prime p in a factorial (n!)

The biggest power of a prime p that divides n! (or in other words, the power of prime p in n!) is given by the sum of quotients obtained by successive division of n by p.

e.g

What is the highest power of 7 that divides 1342!

[1342 / 7] = 191

[191 / 7] = 27

[27 / 7] = 3

Power of 7 = 191 + 27 + 3 = 221

Trick 3: Number of ending zeroes in a factorial (n!)

Number of zeroes is given by the sum of the quotients obtained by successive division of n by 5.

e.g.

What is the number of ending zeroes in 134! ?

[134/5] = 26

[26/5] = 5

[5/5] = 1

Number of ending zeroes = 26 + 5 + 1 = 32