How many consecutive zeros are there at the end of 100! (100 factorial) ?

Solution :

There are 24 zeros on the end of 100!

One solution would be to work this out and count the zeros, well I've done this so you don't have to. The answer is...

9332621544394415268169923885626670049071596826438162146859296389521759999322991560894146397615651828625369792082722375825118520916864000000000000000000000000

Well now you can clearly just count the zeros but actually working out the number is not practical so we need another plan.

The clever bit here is thinking what numbers when multiplied together will end in a zero.
So the product of what numbers when multiplied ends in a zero:
1. When one of the things being multiplied ends in zero itself
2. A number ending in 5 multiplied by an even number

3. 25, 50 and 75 when multiplied by some of the small numbers available eg (4, 2 and 6) generate an extra zero

Below is tabulated the origin of all the zeros:

Number	Zeros	Number	Zeros
100	2	95	1
90	1	85	1
80	1	75	2
70	1	65	1
60	1	55	1
50	2	45	1
40	1	35	1
30	1	25	2
20	1	15	1
10	1	5	1
Total	12	Total	12

So that's it then there are 24 zeros at the end of 100!