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Factors

by Akansha » Sun May 29, 2011 10:30 am
How many different prime numbers are factors of positive integer n?
a. 4 different prime numbers are factors of 2n
b. 4 different prime numbers are factors of n^2

OA is B
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by SoCan » Sun May 29, 2011 10:55 am
1) n could have 3 or 4 prime factors (multiplying by 2 adds a prime factor if n is odd).
2) Taking the root of a perfect square doesn't change the number of prime factors, it just reduces the length. Since we know n is an integer, n^2 is a perfect square, and n must have the same 4 prime factors. Only 2) is sufficient.
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