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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).

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

1. Kaustav Roy says:

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

1. Anish Ray says:

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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