If $M = 2^{2} \times 3^{5}, N = 2^{2} \times 3^{4},$ then the number of factors of N that are common with factors of M is

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Solution

The correct option is D 15
$M = 2^{2} \times 3^{5}$
Number of factor $= (2 + 1) (5 + 1) = 3 \times 6 = 18$
$N = 2^{2} \times 3^{4}$
Number of factor $= (2 + 1) (4 + 1) = 3 \times 5 = 15$
Then the number of factors of N that are common with factors of M is 15

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