Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Number of divisors and Integer.

## Number of divisors and Integer (B.Stat Objective)

The smallest positive integer n with 24 divisors (where 1 and n are also considered divisors of n) is

- 240
- 360
- 420
- 480

**Key Concepts**

Number of divisors

Integer

Least positive integer

## Check the Answer

But try the problem first…

Answer: 360

B.Stat Objective Question 83

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

number of divisors of 420=(2+1)(1+1)(1+1)(1+1)=24

Second Hint

number of divisors of 240=(4+1)(1+1)(1+1)=20

Final Step

number of divisors of 360=(3+1)(2+1)(1+1)=24 and number of divisors of 480=(5+1)(1+1)(1+1)=24 then required number =360.

## Other useful links

- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA

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