Problem Of The “Every So Often”

An interesting problem came up in conversation with a College Preparatory School freshman the other day, so I thought I’d share it with you: 100! (pronounced “one hundred, factorial”) is the result of taking “100 times 99 times 98 times…” and so on, all the way down to “…times three times two times one.” The question is this: when you write it all out, how many zeroes does that number end with? I like this problem because it’s clear that writing it out won’t work; it would be boring, take too long, and you’d invariably make at least one mistake. And the number’s way too big for a calculator to deal with. So… what next? (By the way, January’s Problem Of The Every So Often can be found, with a solution and I’ve posted the problems from a bi-annual puzzle event I host here.)

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