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Different factors of an integer

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Different factors of an integer

by hksam07 » Mon Jan 19, 2009 4:05 pm
Hi everyone, i am new to this forum and i have a DS question...

How many different factors does the integer n have?
(1) n = (a^4)(b^3), where a and b are different positive prime numbers.
(2) The only positive prime numbers that are factors of n are 5 and 7.

don't know where to begin.. :shock:
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by hypik21 » Mon Jan 19, 2009 10:52 pm
IMO A

prime numbers have only itself and 1 as factors, so there are a finite number of solutions regarding the first statement...plug in examples

a=2 b =3

(2^3)(3^4)=(8)(81)

8's factors=(1,8,2,4)
81=(1,81,3,27,9)

try 5^3 and 3^4=(125)(81)
125 - 1,125,5,25
81=1,81,3,27,9

statement 2 is insufficient because the variable can include non-prime numbers as well
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