GATE 2014 CS (CS2) – Question 59

Engineering Mathematics · Discrete Mathematics: Combinatorics (Counting, Recurrence Relations, Generating Functions) · 2 marks · Numerical answer

Find the number of distinct positive integer factors of 2014.

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Correct answer: 8 to 8

Explanation

Factor2014=2×1007=2×19×53, with three distinct prime factors each to exponent1. The divisor-count formula gives(1+1)³=**8**. It includes1and2014as positive divisors.