The number of zeros at the end of 70! is

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answer is A.

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Detailed Solution

70!= 2a×3b×5c×7d×... Now, a= E2 (70!) = [102]+[7022]+[7024]+[7025]+[7026] ⇒ a= 35 +17+8+4+2+1 =67 And, C = E5 (70!)= [705]+[7052]= 14+2=16 ∴ 70! = 267 ×516×3b×7d×... ⇒ 70! = (2×5)16×251×3b×7d×... ⇒ 70! = 1016×251 ×3b×74 ×... Thus, the number of zeros at the end of 70! is 16.

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