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Find the number of factors of $120$ .

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13

14

15

16

answer is D.

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Detailed Solution

120

is a type of composite number so it has more than two factors, unlike a prime number which has only two factors i.e,

1

and the number itself.
But we can express

120

in terms of its prime factors

\Rightarrow 5 \times 3 \times 2 \times 2 \times 2 = 120

Among the

5

main factors given above, there are other factors as well.
Those other factors can be enumerated below:
Now number of factors = highest power of each prime factor multiplied by

1

highest power of other factor

+ 1

.
So, here the highest powers of

5, 3

and

2

are

1, 1

and

3

respectively.
So,

120 (3 + 1) \times (1 + 1) \times (1 + 1) = 16

factors.

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