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If n = 15! + 13, which of the following is a divisor of n?

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rtaha2412
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If n = 15! + 13, which of the following is a divisor of n? [#permalink] New post   23 Dec 2010, 18:39
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If \(n=15!+13\), which of the following is a divisor of \(n\)?

A. 15
B. 14
C. 13
D. 7
E. 2

M03-20

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C
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KarishmaB
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Re: If n = 15! + 13, which of the following is a divisor of n? [#permalink] New post   23 Dec 2010, 19:29
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rtaha2412 wrote:
Which of the following integers is a divisor of(15!+13)?


a 15
b 14
c 13
d 7
e 2


When we say 15!, it just means 1*2*3*4*5*...*13*14*15

So you need to find the integer which is a divisor of
(1*2*3*4*5*...*13*14*15 + 13) = 13 (1*2*3*4*5*...*12*14*15 + 1) We obtain this by taking 13 common.

Hence 13 is definitely a divisor of (15! + 13).
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Re: If n = 15! + 13, which of the following is a divisor of n? [#permalink] New post   23 Dec 2010, 19:34
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It should be C. 15!+13= 13( 1*2*3*....12*14*15+1)
Therefore 13 is the answer
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Re: If n = 15! + 13, which of the following is a divisor of n? [#permalink] New post   24 Dec 2010, 01:23
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rtaha2412 wrote:
Which of the following integers is a divisor of(15!+13)?


a 15
b 14
c 13
d 7
e 2


Similar questions testing the same concept:
factor-factorials-100670.html
gmat-prep-ds-96091.html
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Re: If n = 15! + 13, which of the following is a divisor of n? [#permalink] New post   17 Feb 2023, 13:06
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Bunuel wrote:
15! + 13 is divisible by which of the following ?

A. 15
B. 14
C. 13
D. 7
E. 2

Show Spoiler
What integer is expression 15!+13 evenly divisible by?


Since both 15! and 13 are divisible by 13, 15! + 13 is divisible by 13.

Answer: C
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Re: If n = 15! + 13, which of the following is a divisor of n? [#permalink] New post   13 Aug 2023, 12:56
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If \(n=15!+13\), which of the following is a divisor of \(n\)?

A. 15
B. 14
C. 13
D. 7
E. 2


\(n=15! + 13 = 1*2*3*...12*13*14*15+13\). Since 13 is a factor of both \(15!\) and the additional 13 in the expression, we can conclude that 13 is a divisor of \(n\). In other words, we can factor out 13 from the expression to get \(n=13*(1*2*3*...12*14*15+1)\), hence 13 is definitely a divisor of \(n\).


Answer: C
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Re: If n = 15! + 13, which of the following is a divisor of n? [#permalink]
13 Aug 2023, 12:56
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