Try this beautiful problem from Integer based on Integers and Divisors useful for ISI B.Stat Entrance.

## Integers and Divisors | ISI B.Stat Entrance | Problem-98

The number of positive integers which divide 240 (where both 1 and 240 are considered as divisors) is

- 20
- 18
- 16
- 12

**Key Concepts**

Integer

Divisor

Number theory

## Check the Answer

But try the problem first…

Answer: 20

TOMATO, Problem 98

Challenges and Thrills in Pre College Mathematics

## Try with Hints

First hint

We have to find out the number of positive integers which divide 240.so at first we have to find out the factors of 240…

\(240=2 \times 120\)

\(240=3 \times 80\)

\(240=4 \times 60\)

\(240=5 \times 48\)

\(240=6 \times 40\)

\(240=8 \times 30\)

\(240=10 \times 24\)

\(240=12 \times 20\)

\(240=15 \times 16\)

\(240=20 \times 12\)

\(240=24 \times 10\) …………..

so we notice that the divisors are repeat……..

Can you now finish the problem ……….

Second Hint

We notice that after \(240=15 \times 16\) this stape all the factors are repeats…..so we have to calculate up to \(240=15 \times 16\) step only….

can you finish the problem……..

Final Step

Therefore the total number of positive integers are \(1,2,3,4,5,6,8,10,12,15,20,24,30,40,48,60,80,120,240\) i.e \(20\)

## Other useful links

- https://www.cheenta.com/problem-based-on-lcm-amc-8-2016-problem-20/
- https://www.youtube.com/watch?v=V01neV8qmh4

Google