soumya1989 wrote:
Which of the following is a factor of 18!+1?
A. 15
B. 17
C. 19
D. 33
E. 39
Important Concept #1: If k > 1, and k is a factor (divisor) of N, then k is not a divisor of N+1For example, since 7 is a factor of 350, we know that 7 is not a factor of (350
+1)
Similarly, since 8 is a factor of 312, we know that 8 is not a factor of 313
Important Concept #2: If N is divisible by k, then k is "hiding" within the prime factorization of NConsider these examples:
24 is divisible by
3 because 24 = (2)(2)(2)
(3)Likewise, 70 is divisible by
5 because 70 = (2)
(5)(7)
And 112 is divisible by
8 because 112 = (2)
(2)(2)(2)(7)
And 630 is divisible by
15 because 630 = (2)(3)
(3)(5)(7)
-----ONTO THE QUESTION!---------------------
We're going to use both concepts to ELIMINATE 4 of the 5 answer choices.
A. 15
Since 18! = (18)(17)(16)(
15)....(3)(2)(1), we can see that
15 is a factor (divisor) of 18!
So, according to Concept #1, 15 is NOT a divisor of 18! + 1
ELIMINATE A
B. 17
Since 18! = (18)(
17)(16)....(3)(2)(1), we can see that
17 is a factor (divisor) of 18!
So, according to Concept #1, 17 is NOT a divisor of 18! + 1
ELIMINATE B
C. 19
Leave for now.
D. 33
Since 18! = (18)(17)(16)..(
11)..(
3)(2)(1), we can see that
33 is a factor (divisor) of 18!
So, according to Concept #1, 33 is NOT a divisor of 18! + 1
ELIMINATE D
E. 39
Since 18! = (18)(17)(16)..(
13)..(
3)(2)(1), we can see that
39 is a factor (divisor) of 18!
So, according to Concept #1, 39 is NOT a divisor of 18! + 1
ELIMINATE E
By the process of elimination, the correct answer is C
Cheers,
Brent