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

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).

March 30, 2016

2 comments

  1. 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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