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

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Aashi123's picture
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a) 4658
b)9316
c)2744
d) none of these

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n/a

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n/a

Incognito
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what is the total number of divisors of the number 12^33 x 34^23

d)none of these

truptisaboo's picture
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The number of divisors is

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

truptisaboo's picture
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Last seen: 4 years 43 weeks ago
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The number of divisors is

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

Incognito
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cant u xplain clearly.???

cant u xplain clearly.???

Incognito
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cant u xplain clearly.???

cant u xplain clearly.???

Incognito
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yeah! option D

yeah! option D

Incognito
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the given question must be

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

Incognito
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the given question must be

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

Incognito
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yeah ....it is coming 111792

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

Incognito
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Answer with solution

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.

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