If n is the greatest positive integer for which 4^n is a factor of 8!, then n =?\nOptions:\n(A) 2\n(B) 4\n(C) 6\n(D) 8\n(E) 10
Think hard. Detailed solution:
(A)
8! = 40320\nE.

4^10 = 1048576 (40320/1048576) - this is not a factor of 8!\nD.

4^8 = 65536 (40320/65536) - this is not a factor of 8!\nC.

4^6 = 4096 (40320/4096) - this is not a factor of 8!\nB.

4^4 = 256 (40320/256) - this is not a factor of 8!\nA.

4^2 = 16 (40320/16) - this is a factor of 8!.

Thus, the answer is (A)