zeros...

How many trailing zeros does 4600! have?


The answer is 1148.

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1 solution

The number of trailing zeroes is

4600 5 + 4600 5 2 + 4600 5 3 + 4600 5 4 + 4600 5 5 = 920 + 184 + 36 + 7 + 1 = 1148 \dfrac{4600}{5} + \dfrac{4600}{5^2} + \dfrac{4600}{5^3}+ \dfrac{4600}{5^4}+ \dfrac{4600}{5^5} = 920+184+36+7+1=\boxed{1148}

Note: In the above computation, just consider the whole numbers.

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