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| Math Central | Quandaries & Queries |
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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.
EXERCISE: how?
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!
RD
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