Question

Find the perfect square whose factorial ends in exactly 10 consecutive zeros.

Answer 1

for ten zeros you need five 5's i think

Answer 2

Apparently that answer is 49. Is there a trick to it without a calculator?

Answer 3

according to satellite's logic it shud be b/n 45 nd 50.....

Answer 4

and perfect square b/n them is 49?

Answer 5

for 5! you get 1 zero
for 10! you get an additional zero i.e. 2 zeros in total
for 15! you get 3 zeros in all
for 20! you get 4 zeros in all
for 25! you get 6 zeros (25 = 5*5 it has two 5's)
for 30! - 7 zeros
35! - 8 zeros
40! - 9 zeros
45! - 10zeros
50! - 11 zeros
So, for the factorial of a number to have 10 zeros, it must be one of 45,46,47,48,49
The one that is a square among these is 49

Answer 6

This is the explanation they gave. B is the answer to this question and I don't get what's going on in the explanation.

Answer 7

In general, the number of zeros in the factorial of n, is given by
[n/5] + [n/25] + [n/125] + [n/625] + ....
where [x] represents the greatest integer less than or equal to x

Answer 8

you need 5 fives because there will be more 2's than 5's in any \(n!\) that will give you 10 zeros at the end. for example 10! has 2, 24! has 4 whereas 25! has 6

Answer 9

Thank you everybody everyone! I guess I just have to remember the rule involving the 5s?