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Bunuel
12 Days of Christmas GMAT Competition with Lots of Fun

\(72^4\) has how many positive factors?

A. 5
B. 20
C. 70
D. 96
E. 117




 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

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Explanation-
Factorization of 72--> 2^3 * 3^2
72^4--> 2^12 * 3^8
Positive factors of 72^4--> (12+1) * (8+1) --> 13*9--> 117
Green color- Correct ans is E
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Bunuel
12 Days of Christmas GMAT Competition with Lots of Fun

\(72^4\) has how many positive factors?

A. 5
B. 20
C. 70
D. 96
E. 117






 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

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\(72^4\) is \((9*8)^4\) = \((3^2*2^3)^4\) = (3)^8*(2)^12
# of factors = # of Exponent+1 = (12+1)*(8+1)=117
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Factorizing 72^(4) = 9^(4)*8^(4) = 3^(8)*2^(12)
So, #factors = (8+1)*(12+1) = 117
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\(72^4\) has how many positive factors?

\(72^4\) = \((2^3 * 3^2)^4\) = \(2^(12)\) * \(3^8\)

Factors =multiplication of prime factor power +1
= 13*9=117
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Bunuel
12 Days of Christmas GMAT Competition with Lots of Fun

\(72^4\) has how many positive factors?

A. 5
B. 20
C. 70
D. 96
E. 117




 


This question was provided by GMAT Club
for the 12 Days of Christmas Competition

Win $40,000 in prizes: Courses, Tests & more

 


Factorizing \(72^4\) we get 2^(3*4) * 3^(2*4)
=> 2^12 * 3^8
Number of factors would be (12+1)(8+1) = 13 x 9 = 117

Option E
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