123!’s Zeroes Trick #shorts

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Published on March 9, 2022 7:30:59 PM ● Video Link: https://www.youtube.com/watch?v=aMKxgqtwwVM

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You can determine the number of trailing zeroes on a factorial of ANY size with a pretty simple trick that involves dividing by powers of 5. First, you can do it the hard way, and multiple every number of x! (x * (x - 1) * (x - 2)...) until you're multiplying by 1 at the end, and then just count up the zeroes. Or... you can do it the smart way.

Divide your original number by 5, then 5^2, then 5^3, and when you've got a fractional value, stop and add up the rounded-down whole numbers. And BAM! That's how many trailing zeroes x! has. It really is that easy, even for a 206-digit number like 123!

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