Question

find the number of zeroes at the end of 10*9*8*7*5*6*4*3*32*1

Answer 1

10 is a factor of 5 and 2. In these type of questions you need to know how many 5s and 2s are there in the product. If x is the number of 5s and y the number of 2s, minimum of x and y would be the number of zeroes in any product.
In this question
10*9*8*7*5*6*4*3*32*110 - one 5
9- three 3
8 - three 2
7 - one 7
6 - two 3
5 - one 5
4 - two 2
3 - one 3
1 - one 1
32 - five 2
In total: ten 2s and two 5s.
Minimum of 10 and 2 is 2, which is the number of zeroes in the product.

That is there are two zeros at the end.



Verifying

10*9*8*7*5*6*4*3*32*1=58060800