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by ketkoag » Sun Mar 29, 2009 5:31 am
How many different factors does the integer n have?
(1) n = a^4b^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.

OA: A
Please lemme know whther (4-1)(3-1) is the number of factors if we take statement 1.
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by scoobydooby » Sun Mar 29, 2009 6:45 am
1) n = a^4b^3
no of factors: (4+1)*(3+1)=5*4=20
sufficient

2) The only positive prime numbers that are factors of n are 5 and 7
we do not know the powers of the prime factors 5 and 7, so cant find no of factors
not sufficient

hence A

if n=a^p* b^q, where a and b are prime factors, total number of factors is given by (p+1)*(q+1)
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