Question- How many zeros are there in the product of all the natural numbers right from 1 to 1962 or in short in 1962! ?(adsbygoogle = window.adsbygoogle || []).push({});

Attempt-

Well,

The product as a product of prime numbers, will denoted as -

Let the product be N,

N = 2^{a1}. 3^{a2}. 5^{a3}. ....... p^{ax}

As far as i see it we will have to count the number of 5s and 2s that occur in the product N's representation above and also the factors which will yield 5s or 2s.So by far we are concerned only to the numbers a_{1}and a_{3}.And here lies my problem, how will we calculate the number of occurrences and also figure out that how many other factors will yield how many 5s or 2s ?

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# Count my zeros please :P!

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