RMO 2

Number Theory Level 3

How many powers of 5 are contained in 1000!?


The answer is 249.

Manas Vema by manas vema , 21, India

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2 solutions

Ramiel To-ong
Sep 19, 2015

nice solution

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There are 200 multiples de 5 between 1 and 1000(both inclusive), there are 40 multiples de 25=5^2 between 1 and 1000(both inclusive), there are 8 multiples of 125=5^3 between 1 and 1000(both inclusive), and 1 multiple of 625=5^4 between 1 and 1000(both inclusive). 200 + 40 +8 +1 = 249...

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