Math CentralQuandaries & Queries


Question from Wilson:
How can I find the last non cero digit from a factorial calculation of a big number.
For example 10! = 3628800, the last non cero digit is 8. What is the last non cero digit of 10! ??

This is a fairly subtle problem. In most cases, finding the last nonzero digit of (n+1)! from n and the last nonzero digit of n! is straightforward. It would be very easy to find the last digits of the product of the natural numbers up to N that were not divisible by 5. After N=2 they loop with a period of 8 [omitting values of N as well that end in 0 or 5]

EXERCISE: prove this.

This can be extended to include factors of 10, 100, etc provided the last nonzero digit is not 5.


However, when we multiply by something ending in 5, 50, 500, etc we must be careful - note that 14 x 5 = 70 while 24 x 5 = 120. Multiplying by numbers ending in 25, 125... is even trickier.

Here I pass the problem back to you.

Good Hunting!

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