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Which of the following number has the maximum number of divisors?

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108

154

answer is A.

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Detailed Solution

108 = 2 \times 2 \times 3 \times 3 \times 3 = 2^{2} \times 3^{3}

$99 = 3 \times 3 \times 11 = 3^{2} \times 11$

$154 = 2 \times 7 \times 11$

$44 = 2 \times 2 \times 11 = 2^{2} \times 11$

$d (N) =$

$(A) (2 + 1) \cdot (3 + 1) = 12$

$(B) (2 + 1) \cdot (1 + 1) = 6$

$(C) (1 + 1) \cdot (1 + 1) \cdot (1 + 1) = 8$

$(D) (2 + 1) \cdot (1 + 1) = 6$ .

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