The number of divisors of 2100 is ____.

GATE 2015 · Discrete Mathematics · Number Theory · easy

Answer: The number of divisors of 2100 is 36.

1. Prime factorisation of 2100: 2100 = 2 * 1050 = 2 * 2 * 525 = 4 * 525 = 4 * 3 * 175 = 4 * 3 * 5 * 35 = 4 * 3 * 5 * 5 * 7 = 2^2 * 3^1 * 5^2 * 7^1.
2. Apply divisor count formula: tau(2100) = 3 * 2 * 3 * 2 = 36.