Pls help to explain this prob

[Jason.tuyj]

If n is the greatest positive integer for which 2^n is a factor of 10!, then n =
A. 2 B. 4 C. 6 D. 8 E. 10

[mithunsam]

10! = 1*2*3*4*5*6*7*8*9*10 = 1*2*3*(2^2)*5*(2*3)*7*(2^3)*9*(2*5) = 1*3*5*3*7*9*5*(2^8) [grouping all 2s together]

10! has eight 2s in it. Therefore n=8 is the answer.

[tim]

Thanks mithunsam!