Question

Given that n! Has 13 zeroes, find the minimum and maximum value of n.

Answer 1

50! has 12 zeros 
now let take 55!
55/5=11
55/25=2
ie 55! has 13 zeros
now take 60!
60/5=12
60/25=2.4
ie 60! has 14 zeros 
so take 59!
59/5=11.8
59/25=2.36
ie 59! has 11+2=13 zeros 
so max=59
min=55

Answer 2

The correct answer is minimum = 55 and maximum = 59.

Given: n! has 13 zeroes.

To Find: Minimum and maximum value of n.

Solution:

As n! has 13-0's then it should also have 13-2's and 1's.

Ans as we can find that 50! has 12 zeroes.

Now, we can find that 55! has 13-5's and 50-2's.

So, minimum value of n is 55.

And maximum is 59. Because 60! has 14-5's so it will result in 14 zeroes.

Hence, our final answer is minimum = 55 and maximum = 59.

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