The number of positive factors of $2520$ excluding unity is

48

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45

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46

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47

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Solution

The correct option is D $47$
$2520 = 8 \times 315 = 8 \times 9 \times 35 = 2^{3} \times 3^{2} \times 5 \times 7$
Hence, number of positive factors of $2520$ excluding $1$ are $= (3 + 1) (2 + 1) (1 + 1) (1 + 1) - 1 = 4 \times 3 \times 2 \times 2 - 1 = 47$

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