The product of the first twelve positive integers is

Hi All,

We're told to take the PRODUCT of the first 12 positive integers. We're asked which of the following is NOT divisible into that product. This question is best handled with Prime Factorization.

To start, the GMAT would never expect you to actually calculate a product that was so big, so there must be some other way to get to the answer. For a number to divide into another number, the larger number must have ALL of the smaller number's prime factors (including duplicates).

For example, we know that 50 divides into 100 because....
50 = (2)(5)(5)
100 = (2)(2)(5)(5)

All of the prime factors of 50 (including duplicates) ARE in 100.

By Prime Factoring the Answer choices, we can see that Answer E: 34 = (2)(17). However, there is NO 17 in the product of the first 12 positive integers (the largest prime factor would be 11). Thus, that is the answer that won't divide evenly into that larger product.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorLU wrote:The product of the first twelve positive integers is divisible by all of the following EXCEPT?

A. 210
B. 88
C. 75
D. 60
E. 34

Since the product of the first 12 integers does not have a 17 in the prime factorization, that product is not divisible by 34, which is 17 x 2.

Answer: E