# How To Find First and Second Non Zero Digits In A Factorial - Hemant Malhotra

•  Find last non zero digit of N! Represent N = 5a +b form then last non zero digit will be  2a x a! x b!

Find last non zero digit of 21!

21 = 5 x 4 + 1
so a = 4 and b = 1

so last non zero digit =24 x 4! x 1!
16 x 24 x 1 so last non zero digit = 4

Find last non zero digit of 34!

34 = 5 x 6 + 4
So a = 6 and b = 4 so 26 x 6! x 4!
Now we need to find the last non zero digit  in 6!  so 6 = 5 x 1 + 1
so a=1 and b=1
so 21 x 1! x 1! = 2
now we know that 6! = 720 so last non zero digit is 2 so no need to do this
so 26 x 2 x 4!
27 x 24 = 128 x 24 so last digit=2

Concept 2 -

 Find last two non zero digits of N! Express N = 5a + b then last two non zero digits will be 12a x a! x (5a + 1)(5a + 2) ... (5a + b)

EXAMPLE-  find last two non zero digits of 23!

23 = 5 x 4 + 3
here a = 4 and b = 3
so 124 x 4! x (5 x 4 + 1)(5 x 4 + 2) (5 x 4 + 3)
124 x 4! x 21 x 22 x 23
now multiple and find last two digits

NOTE 1 -last two non zero digits of

5! = 12
25! = 84
125! =88

Last non zero digits

(10!) = 8
(20!) = 4
(30!) = 8
(40!) = 2
(50!) = 2
(60!) = 6
(70!) = 8
(80!) = 8
(90!) = 2
(100!) = 4

Example- if u want to find last non zero digit of 21!

You know last non zero digit of 20! is 4
so 21! = 21 x 20!
21 x 4 = > 4 is the last non zero digit

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