The number of distinct positive integral factors of 2014 is _______________________

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Official answer: 8

Discrete Mathematics

First, find the prime factorization of $2014$ :

2014 = 2 \times 1007

1007 = 19 \times 53

Since $2, 19,$ and $53$ are all prime numbers, the prime factorization of $2014$ is:

2014 = 2^1 \times 19^1 \times 53^1

The total number of positive integral divisors is given by:

d(2014) = (1 + 1)(1 + 1)(1 + 1) = 2 \times 2 \times 2 = 8

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This Discrete Mathematics previous year question is Q49 of the GATE CSE 2014 Set 2 paper. Find more GATE CSE PYQs on Discrete Mathematics in Engineering Mathematics, or browse all GATE CSE PYQs.

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Discrete Mathematics has 50 GATE CSE PYQs across 23 papers from 2011 to 2026. 6 of them are 2-mark NAT questions like this one, and GATE CSE 2014 Set 2 has 3.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.