Find the divisors of 1980 .

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answer is A.

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Detailed Solution

Concept: We will use the prime factorization of 1980 to identify every divisor in this question. The numbers known as divisors or factors are those that, when divided, split the original number exactly and without any remainder. Contrary to prime factors, which only have one extra component in addition to the number itself, composite factors are composed of several prime factors. A number can be divided by either both separately or both jointly.
Finding the 1980 divisors is the next step. All of its components, whether prime or composite, will be found. Since factors and divisors are interchangeable, they totally divide the numbers without leaving a residual.
So, in order to discover the factors or divisors, we must first identify all of the 1980 prime factors.
Hence, factoring 1980:
1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990 and 1980.
So, the total number of divisors of 1980 are 35.
Hence, the correct answer is 1) 35

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