ankitranjan wrote:
Find the number that divides 16!+1?
A. 7
B. 11
C. 17
D. 6
E. 18
We need to determine which one of the numbers in the given answer choices divides into 16! + 1. In other words, which one is a factor of 16!+1. To determine this, we must recognize that 16! and 16! + 1 are consecutive integers, and consecutive integers will never share the same prime factors. Thus, 16! and 16! + 1 must have different prime factors.
However, rather than breaking 16! factorial into primes, we can look at the answer choices to determine which choice is not a factor of 16!. Since 16! = 16 x 15 x 14…5 x 4 x 3 x 2 x 1, we see that choices A, B, and D are factors of 16! Since 18 = 2 x 9, 2 and 9 are also factors of 16!. However, none of these numbers (6, 7, 11, and 18) will be a factor of 16! + 1, so the only number that can be a factor of 16! + 1 is 17.
Answer: C
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