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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

But try the problem first…

Source

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 $20$