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# If P represents the product of the first 15 positive

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If P represents the product of the first 15 positive [#permalink]  17 Oct 2005, 17:23
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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

VP
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E.
x = 1*2*3*4.....*15

factorise above in unique prime factorization.
x will be multiple of a number if its prime factorization has all the prime factors of the divisor.

E - 57 = 19 * 3
19 is not a factor of x. Therefore, 57 wont divide it(57 not a factor).
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I think best approach is to break each answer into different factors less than equal to 15.. one with a factor greater than 15 is the odd one out...

A) 99 = 9*11 (both factors <15)
B) 84 = 12*7 (both factors less than 15)
C) 72 = 12 * 8
D) 65 = 13 * 5
E) 57 = 19 * 3 (19 is greater than 15)

Ans. E
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-Vikram

Last edited by vikramm on 17 Oct 2005, 17:35, edited 1 time in total.
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Ans is E.

factor 57 into primes 3 and 19
15! is not a multiple of 19
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Any number that cannot be expressed in terms of a product of numbers btw 1 to 15 (each # occuring only once) will not divide the product 1*2*...*15

A. 99 - 11*9
B. 84 - 2*6*7
C. 72 - 2*4*9
D. 65 - 5*13
E. 57 - 3*19
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