The number of positive integers which divide \(240 \) is-
(A) 18; (B) 20; (C) 30; (D) 24;
We use the formula for computing number of divisors of a number:
Step 1: Prime factorise the given number
\(240 = 2^4 \times 3^1 \times 5^1 \)
Step 2: Use the formula for number of divisors: \((4+1) \times (1+1) \times (1+1) = 20 \)
Answer: (B) 20;
Why this formula works? Basically, we are adding 1 to each exponent of each prime factor and then multiplying them. Refer to a discussion on Number Theoretic Functions (in any standard number theory book like David Burton’s Elementary Number Theory).