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 Let's think first. Stream of consciousness:
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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!
So, the answer is (A).
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