Find the number of factors of 1728

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Solution

The correct option is B 28
If the prime factorisation of a composite number $N = a^{m} \times b^{n} \times c^{o} . . . .$ , the number of its factors $= (m + 1) (n + 1) (o + 1) . . . .$
Prime factorisation of $1728 = 2^{6} \times 3^{3}$
So, number of factors of $1728 = (6 + 1) \times (3 + 1) = 7 \times 4 = 28$

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