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FACTOR QUESTION! SMALLEST POSSIBLE VALUE OF N?

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FACTOR QUESTION! SMALLEST POSSIBLE VALUE OF N?

by JohnQ2011 » Thu Mar 10, 2011 8:55 am
Hi,

Looking for some help and explanation of process for this question.

Thanks!

If both 5^2 (25) and 3^3 (27) are factors of n x 2^5 x 6^2 x 7^3, what is the smallest possible positive value of n?

a) 25
b) 27
c) 45
d) 75
e) 125

ANSWER IS {D} - IF ANYONE CAN HELP WITH DETAILED METHODOLOGY AND WORK THAT WOULD BE GREAT!
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by srcc25anu » Thu Mar 10, 2011 10:49 am
if we break the RHS of the equation to its smallest prime factor terms, we get 2^5 * 2^2 * 3^2 * 7^3 *n (sine 6 can broken down as 3*2). From 6^2, we get 2 powers of 3.
the question asks us for 5^2 * 3^3 i.e 2 powers of 5 and 3 powers of 3
from the above we get 2 powers of 3
remaining we need to get one 3 and 2 5's therefore smallest value of n can be 5^2 * 3 or 25*3 = 75
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