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18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

GMAT Diagnostic Test Question 9 Field: Arithmetic Difficulty: 650

Which of the following is a factor of 18!+1?

A. 15 B. 17 C. 19 D. 33 E. 39

Solution 1: Because 19 is a prime, applying Wilson's theorem, we have 19 is a factor of (19-1)! + 1 = 18! +1. Solution 2: We have 15 = 3*5, 33= 3*11, 39 = 3*13. Therefor, 15, 17, 33, 39 are factors of 18! = 1 * 2 *3 * 4 * 5 * ... * 17 * 18. Because 18! +1 and 18! are co-prime, 15, 17,33 and 39 is not a factor of 18! + 1. The answer must be C (19).

18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

Answer: C

I Find it difficult to understand the explaination..is there any other way to solve this question...

18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

Answer: C

I Find it difficult to understand the explaination..is there any other way to solve this question...

Frankly, solution provided is the easiest from my point of view.

We have that each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1. Therefore, only 19 can be a factor of 18!+1. Since one of the options must be correct and we know that A, B, D and E are not, then C must be correct.

18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

Answer: C

I Find it difficult to understand the explaination..is there any other way to solve this question...

Frankly, solution provided is the easiest from my point of view.

We have that each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1. Therefore, only 19 can be a factor of 18!+1. Since one of the options must be correct and we know that A, B, D and E are not, then C must be correct.

17 is a prime no. I agree with 15= 5*3, 33=11*3, 39=13*3

Bunuel wrote:

lindt123 wrote:

bb wrote:

18! and 18!+1 are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1.

Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1.

Answer: C

I Find it difficult to understand the explaination..is there any other way to solve this question...

Frankly, solution provided is the easiest from my point of view.

We have that each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1. Therefore, only 19 can be a factor of 18!+1. Since one of the options must be correct and we know that A, B, D and E are not, then C must be correct.

17 is a prime no. I agree with 15= 5*3, 33=11*3, 39=13*3

Bunuel wrote:

lindt123 wrote:

I Find it difficult to understand the explaination..is there any other way to solve this question...

Frankly, solution provided is the easiest from my point of view.

We have that each 15, 17, 33, and 39 IS a factor of 18!, thus NOT a factor of 18!+1. Therefore, only 19 can be a factor of 18!+1. Since one of the options must be correct and we know that A, B, D and E are not, then C must be correct.