# what is the total number of divisors of the number 12^33 x 34^23 x 2^47

a) 4658

b)9316

c)2744

d) none of these

n/a

The number of divisors is 111,792 so hence the answere is choice D none of these .

The number of divisors is 111,792 so hence the answere is choice D none of these .

cant u xplain clearly.???

cant u xplain clearly.???

yeah! option D

the given question must be boiled down to its prime factors :

i.e

12^33*34^23*2^47 = (3*4)^33*(2*17)^23*2647

= 2^136 * 3^33 * 17^23

Now the nos of factors are:

(136+1)* (33+1) * (23+1) { product of powers of prime factors+1 )

= 137*34*24 = 111792

the given question must be boiled down to its prime factors :

i.e

12^33*34^23*2^47 = (3*4)^33*(2*17)^23*2647

= 2^136 * 3^33 * 17^23

Now the nos of factors are:

(136+1)* (33+1) * (23+1) { product of powers of prime factors+1 )

= 137*34*24 = 111792

yeah ....it is coming 111792 ....137*34*24

d)none of these(Ans-111792).

sol:-12^33*34^23*2^47=2^66*3^33*2^23*17^23*2^47 (as 12=2^2*3,34=2*17)

=2^136*3^33*17^23

Hence no. of factors=(136+1)(33+1)(23+1)

=137*34*24=111792 ans.

d)none of these