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prime factors

by joannabanana » Mon Oct 11, 2010 4:01 am
If n is a positive integer less than 200 and 14n/60 is an integer, then n has how many different positive prime factors?
a. one
b. three
c. five
d. six
e. eight

[spoiler]ans: b[/spoiler]
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by Rahul@gurome » Mon Oct 11, 2010 4:41 am
14n/60 = 7n/30, which implies 30 should be a factor of n because 30 is not a factor of 7.
Possible values of n are 30, 60, 90, 120, 150, 180.
30 = 2*3*5
60 = 2^2*3*5
90 = 2*3^3*5 and so on, so we can see that all these integers have 3 prime factors 2, 3 and 5.

[spoiler]Therefore, correct answer is (B).[/spoiler]
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