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In how many ways can 2744 be resolved as a product of two factors?

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answer is D.

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Detailed Solution

Concept: Concept used here is mainly factorization. We will apply the prime factorization method.If the prime factorisation of a number

N = a^{m} \times b^{n}

. . . . . . then number of factors is

(m + 1) \times (n + 1)

. . . . and so on
Prime factor of 2744 e.g (

)
The Prime factorizations of

So, the number of factors of 2744 is

= (3 + 1) \times (3 + 1) = 4 \times 4 = 16

Thus it can be resolved by a product of two factors =

Hence, the correct option is (4).

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