# Number of Positive Divisors (Tomato objective 98)

The number of positive integers which divide $$240$$ is-
(A) 18; (B) 20; (C) 30; (D) 24;

Discussion:

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: $$(4+1) \times (1+1) \times (1+1) = 20$$

Note:

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).

## 2 Replies to “Number of Positive Divisors (Tomato objective 98)”

1. Sir, can you plzz suggest me how to do TOMATO OBJECTIVE NO. 99 .i.e. Sum of all positive divisors of 1800

1. You can find the formula for the sum in any standard book namely An Excursion in Mathematics,Challenges and Thrills of Pre-College Mathematics.

Or you may surf up the google
Use the keyword-“Sum of divisors”

Hope this helps