DS

[ketkoag]

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.

[scoobydooby]

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)