Finding the right most non zero digit of N!

Finding the right most non zero digit of N!.

If we have to find the right most non zero digit of N! we have two ways:
1. Removing all the 10’s.
2. Using direct formula.

Let’s understand this with an example :

Q.Find the right most non zero digit of 16!

Approach 1:
We will try to remove all 10’s so that we can get non zero digit .
16! = 2¹⁵ × 3⁶ × 5³ × 7² × 11 × 13

How many 10’s will be made ?
As 10 = 2 × 5
So limiting factor (factor which will decide ) will be 5 as exponent of 5 is lesser than that of 2
So 5³ so three 10’s will be made
So 10³ will be made

So now rewrite 16! as
= 10³ × {2¹² × 3⁶ × 7² × 11 × 13}

So terms inside { } will decide the non zero digit
Now just consider the unit digits of each
2¹² = 6
3⁶ = 9
7² = 9
11¹ = 1
13¹ = 3
Product of all will yield unit digit as 8

So 8 is the right most non zero digit

Approach 2 :
We have a formula for such Questions
Write N = 5a + b form and right most non zero digit will be
2^a × a! × b!

So
16 = 5 × 3 + 1
So right most non zeros digit is
2³ × 3! × 1!
=8 (unit digit only )

So when the number is quite big we can use the formula for convenience.