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# Number of Positive Divisors | Tomato objective 98

This is an objective problem from TOMATO based on finding the Number of Positive Divisors.

Problem:

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).

## By Dr. Ashani Dasgupta

Ph.D. in Mathematics, University of Wisconsin, Milwaukee, United States.

Research Interest: Geometric Group Theory, Relatively Hyperbolic Groups.

Founder, Cheenta

## 2 replies on “Number of Positive Divisors | Tomato objective 98”

Kaustav Roysays:

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

Anish Raysays:

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

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