Determine the number of divisors of 600.

GATE 1995 · Discrete Mathematics · Number Theory · medium

Answer: The number of divisors of 600 is 24.

1. Prime factorisation of 600: 600 = 2 * 300 = 2 * 2 * 150 = 2 * 2 * 2 * 75 = 8 * 75 = 8 * 3 * 25 = 2^3 * 3^1 * 5^2.
2. Apply the divisor count formula: tau(600) = tau(2^3 * 3^1 * 5^2) = (3+1) * (1+1) * (2+1) = 4 * 2 * 3 = 24.