This looks like a job for prime factorization!

144 = (2)(2)(2)(2)(3)(3)
The greatest prime factor = x = 3

96 = (2)(2)(2)(2)(2)(3)
The greatest prime factor = y = 3

We get:
Quantity A: 3
Quantity B: 3

Answer: C

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The greatest prime factor of 144 is x
The greatest prime factor of 96 is y

Quantity A	Quantity B
x	y

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Kudos for the right answer and explanation
See more on this topic Numbers Comprehension

Qt A

Factors of \(144 = 1 , 2 , 3 , 4 , 6 , 8 , 12 , 18 , 24 , 36 , 48 , 72 , 144\)

Greatest prime factor \(= 3\)

Qt B

Factors of \(96 = 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 32 , 48 , 96\)

Greatest prime factor \(= 3\)

Qt A = Qt B

Answer C

The greatest prime factor of 144 is x

The greatest prime factor of 96 is y

Quantity A	Quantity B
x	y

A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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