Problem with Zero

8589934592 * 116415321826934814453125 in this product there is no 0 (zero) in two numbers. How many zeros does it contain when the problem is solved?


The answer is 33.

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1 solution

Ratul Pan
Mar 26, 2016

The simplest way of counting the number of trailing zeroes is to factorise and see the number of powers of 5 and 2.
In the first number 8589934592 there is no power of 5 because it does not end with 5 or 0.
Factorising 8589934592 , we find that it is 2 33 2^{33}
Factorising 116415321826934814453125 , we find that it is 5 33 5^{33}
Hence the product will have 33 \boxed{33} zeroes at the end.


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