This is an objective problem from TOMATO based on finding the Number of Positive Divisors.
The number of positive integers which divide 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
Step 2: Use the formula for number of divisors:
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).