Official PYQ · 1995Q7(A)Sets, Relations and FunctionsNAT1 mark

GATE CS 1995 Q7(A) — Sets, Relations and Functions

Determine the number of divisors of

600.

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Answer: 24

To find the number of divisors of $600$ , we first find its prime factorization.

Expressing $600$ as a product of prime factors:

600 = 6 \times 100 = (2 \times 3) \times (2^2 \times 5^2) = 2^3 \times 3^1 \times 5^2

For any positive integer $N$ with prime factorization $p_1^{a_1} \cdot p_2^{a_2} \cdots p_k^{a_k}$ , the total number of positive divisors is given by the formula:

d(N) = (a_1 + 1)(a_2 + 1) \cdots (a_k + 1)

Applying this formula to $600 = 2^3 \times 3^1 \times 5^2$ :

d(600) = (3 + 1)(1 + 1)(2 + 1) = 4 \times 2 \times 3 = 24

Thus, the number of divisors of $600$ is 24.

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Published 10 Oct 2026

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