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E.g you have to find the number of trailing zeros of 28! in base 5.

How would you go about it without writing 28! in base 5? Is there a certain step by step method?

I already wrote 28! as a product of its primes.

28! = 2^25 * 3^13 * 5^6 * 7^4 * 11^2 * 13^2 * 17 * 19 * 23

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The number of trailing zeros of an integer $n$ expressed in base-$b$ is equal to the greatest value of $k$ such that $b^k \mid n$, so in this case you need to find the greatest power of $5$ that divides $28!$.

By finding its entire prime factorisation, you've created far more work for yourself than you needed to!

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  • $\begingroup$ Thanks I will give that method a go. $\endgroup$ – user665168 Apr 23 at 21:20

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