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

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Which of the following is NOT a factor of 20!? [#permalink]  05 Nov 2017, 01:44
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Question Stats:

44% (01:00) correct 55% (00:20) wrong based on 9 sessions
Which of the following is NOT a factor of 20! ?

A. 17
B. 21
C. 25
D. 29
E. 42
F. 51
G. 85
H. 121

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[Reveal] Spoiler: OA
D. and H.
[Reveal] Spoiler: OA
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Re: Which of the following is NOT a factor of 20!? [#permalink]  05 Nov 2017, 03:05
In order not to be a factor of 20!, a number must no be between 1 and 20 and it cannot be computed as the product of numbers contained in 20!. Ths means that 29, which is prime and greater than 20 and 121 which is 11*11 and in 20! we have just one 11 are not factors of 20! Answers D and H.

The others are either between 1 and 20 such as 17 or they can be computed as products of factors of 20! such as 42 = 6*7.
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Re: Which of the following is NOT a factor of 20!? [#permalink]  24 Nov 2018, 15:12
Hi, i think that 25 could not be a factor of 20! because it is 5*5 but we have just one 5, am i right?
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Re: Which of the following is NOT a factor of 20!? [#permalink]  24 Nov 2018, 19:43
Expert's post
shahab1987 wrote:
Hi, i think that 25 could not be a factor of 20! because it is 5*5 but we have just one 5, am i right?

No.. we have four 5 in 20! as 20! = 1*2*3*4*5*6..*10*11*...15*16..*20, so one five comes from each of 5, 10, 15 and 20. so $$5^4$$

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

A. 17.......$$20!=1*2*.....17*...20$$.. YES

B. 21=3*7.......$$20!=1*2*3.....7*...20$$.. YES

C. 25=5*5.......$$20!=1*2*...*5*..10*.....*15*....20$$.. YES

D. 29.... since 29 is a PRIME number and 20! contains number only till 20, 29 will NOT be there in 20!

E. 42=2*3*7.......$$20!=1*2*3*.....7*...20$$.. YES

F. 51=3*17.......$$20!=1*2*3.....17*...20$$.. YES

G. 85=5*17.......$$20!=1*2*3*4*5*.....17*...20$$.. YES

H. 121=11*11...........$$20!=1*2*.....11*...20$$.. NO, as we have only one 11.

so D and H
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: Which of the following is NOT a factor of 20!? [#permalink]  24 Nov 2018, 22:33
D and H is the answer. Nice question, thanks for adding it!
Re: Which of the following is NOT a factor of 20!?   [#permalink] 24 Nov 2018, 22:33
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# Which of the following is NOT a factor of 20!?

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