Question

If 'n' factorial has exactly 20 zeroes at the end, Find 'n', How many such 'n' are there?

Answer 1

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Answer 2

Answer:

If 'n' factorial has exactly 20 zeroes at the end, then the value of 'n' can be 85, 86, 87, 88, 89. And FIVE 'n' are possible.

Step-by-step explanation:

The number of zeroes on the end of base 10 illustration of n! is similar to the most power of 5 dividing n!, that is given by [n/5]+[n/5²]+[n/5³]+……, which is without a doubt a finite sum (where [ ] is a step function).

We notice that (100/5) =20, and subsequently n have to be much less than 100.

Also [80/5]+[80/5²] = 16+3 = 19. Hence the least value of n for which the above sum is 20 have to be 85.

All the possible values of n are therefore given as 85, 86, 87, 88, 89.

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