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# Which of the following is NOT a factor of 20!?

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Math Expert
Joined: 02 Sep 2009
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Which of the following is NOT a factor of 20!?  [#permalink]

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17 Aug 2017, 00:03
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15% (low)

Question Stats:

73% (00:54) correct 27% (00:55) wrong based on 132 sessions

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Which of the following is NOT a factor of 20!?

I. 29
II. 85
III. 121

A. I only
B. II only
C. III only
D. I and II
E. I and III

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Re: Which of the following is NOT a factor of 20!?  [#permalink]

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17 Aug 2017, 00:21
1.29
There is no 29 in 20!. So it is not a factor
2.85
85 can be written as 5*17. Both numbers can be found in 20!.So it is a factor
3.121
121 =11*11. There is only one 11 in 20! So it is not a factor of 20!

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Which of the following is NOT a factor of 20!?  [#permalink]

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17 Aug 2017, 11:45
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
20! has to have it's units digit be a 0

The only divisible factor of 0 is 5 and 0, so the answer that fits this is 85. So, the answer is (E): I and III
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Re: Which of the following is NOT a factor of 20!?  [#permalink]

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18 Aug 2017, 00:04
29 cannot be a factor of 20!

85 is a factor since 5*17 = 85 and 5 and 17 are factors of 20!

121 = 11*11

hence cannot be a factor of 20!

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Re: Which of the following is NOT a factor of 20!?  [#permalink]

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18 Aug 2017, 00:49
Bunuel wrote:
Which of the following is NOT a factor of 20!?

I. 29
II. 85
III. 121

A. I only
B. II only
C. III only
D. I and II
E. I and III

29 --- prime number , so it won't be divisible ..
85 --17 * 5 -- both are part of 20! --so yes
121 -- 11 * 11 -- only one 11 is possible in 20!--No
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Re: Which of the following is NOT a factor of 20!?  [#permalink]

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24 Aug 2017, 12:47
Bunuel wrote:
Which of the following is NOT a factor of 20!?

I. 29
II. 85
III. 121

A. I only
B. II only
C. III only
D. I and II
E. I and III

Since 20! does not contain a prime factor of 29, 29 is not a factor of 20!

Since 85 = 17 x 5, and 20! contains both prime factors of 17 and 5, 85 is a factor of 20!.

Since 121 = 11^2, and 20! does not have 2 prime factors of 11, 121 is not a factor 20!.

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Re: Which of the following is NOT a factor of 20!?   [#permalink] 24 Aug 2017, 12:47