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The factorial expression 13!/7! is not divisible by which of

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Carcass
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The factorial expression 13!/7! is not divisible by which of [#permalink] New post   05 Aug 2020, 12:13
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The factorial expression \(\frac{13!}{7!}\) is not divisible by which of the following integers?

(A) 3
(B) 5
(C) 6
(D) 7
(E) 9
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D
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GreenlightTestPrep
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Re: The factorial expression 13!/7! is not divisible by which of [#permalink] New post   05 Aug 2020, 12:48
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Carcass wrote:
The factorial expression \(\frac{13!}{7!}\) is not divisible by which of the following integers?

(A) 3
(B) 5
(C) 6
(D) 7
(E) 9


\(\frac{13!}{7!} = \frac{(13)(12)(11)(10)(9)(8)(7)(6)(5)(4)(3)(2)(1)}{(7)(6)(5)(4)(3)(2)(1)}=(13)(12)(11)(10)(9)(8)\)

(13)(12)(11)(10)(9)(8) is divisible by 3, because (13)(12)(11)(10)(9)(8) = (13)(12)(11)(10)(3)(3)(8). Eliminate A
(13)(12)(11)(10)(9)(8) is divisible by 5, because (13)(12)(11)(10)(9)(8) = (13)(12)(11)(5)(2)(9)(8). Eliminate B
(13)(12)(11)(10)(9)(8) is divisible by 6, because (13)(12)(11)(10)(9)(8) = (13)(7)(2)(11)(10)(9)(8). Eliminate C
(13)(12)(11)(10)(9)(8) is divisible by 6, because (13)(12)(11)(10)(9)(8) = (13)(12)(11)(10)(9)(8). Eliminate E

Answer: D

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Brent
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Re: The factorial expression 13!/7! is not divisible by which of [#permalink]
05 Aug 2020, 12:48
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