Prime Numbers problem

[divyalr]

Hi Folks,
I found this problem in the Advanced GMAT problems material. Please help solving it using a shortcut method.

Q> if p and q are primes, how many divisors does the product p^3.q^6 have?

Choices>
a) 8
b) 12
c) 18
d) 28
e) 36

Answer is d.

[xcusemeplz2009]

divisors will be
p^3=> 3 diff divisors
q^6=> 6 diff div
p^3*q^6=>18 diff div
and 1
adding 3+6+18+1=28

D is correct

[aa2kash]

Hi Folks,
I found this problem in the Advanced GMAT problems material. Please help solving it using a shortcut method.

Q> if p and q are primes, how many divisors does the product p^3.q^6 have?

Choices>
a) 8
b) 12
c) 18
d) 28
e) 36

Answer is d.

@Divya
no of divisors is multiplication of (powers of each primes +1)

Here power of p is 3 and that of q is 6
No of divisors=(p+1)(q+1)=(3+1)(6+1)=28.