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Multiples

by selango » Fri Jul 23, 2010 1:09 am
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
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by surajgarg » Fri Jul 23, 2010 1:14 am
selango 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
Lets factorize the answer choices

99 - 3 x 3 x 11
84 - 3 x 4 x 7
72 - 2 x 2 x 2 x 3 x 6
65 - 5 x 13
57 - 3 x 19

Note that 57 has a factor '19' which will not feature in the first 15 positive integers. Hence P cannot be a multiple of 57.

Hence thats the answer.
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