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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

Answer: (B) 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”

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

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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