A factor of n is a number which when multiplied by another number gives us the number n. The correct option is B, 2.
What is a factor?
A factor of n is a number which when multiplied by another number gives us the number n.
For the result of ∛(144/y) to be a whole number the value of 144/y should be a perfect cube.
Since the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. Also, the numbers that are a perfect cube under 144 are 1,8,27,64, and 125.
Now, divide 144 by each factor to get see which results in a perfect cube.
144/1 = 144,
144/2 = 72,
144/3 = 48,
144/4 = 36,
144/6 = 24,
144/8 = 18,
144/9 = 16,
144/12 = 12,
144/16 = 9,
144/18 = 8 (Perfect Cube),
144/24 = 6,
144/36 = 4,
144/48 = 3,
144/72 = 2,
144/144 = 1 (Perfect Cube).
Hence, the correct option is B, 2.
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