product

shashank.ism wrote:If P represents the product of the first 15 positive integers, then P is not a multiple of:

A) 99
B) 84
C) 72
D) 65
E) 57

Let’s look at the answer choices.

Since 99 = 9 x 11, both of which are included in the product of the first 15 integers, we see that P is a multiple of 99.

Similarly, since 84 = 42 x 2 = 21 x 4 = 7 x 3 x 4, we see that P is a multiple of 84.

Since 72 = 36 x 2 = 6 x 3 x 2 x 2 = 6 x 3 x 4, we see that P is a multiple of 72.

Since 65 = 5 x 13, we see that P is a multiple of 65.

Since 57 = 19 x 3, and since the product of the first 15 integers does not have a prime factor of 19, P cannot be a multiple of 57.

Answer: E