 Try this beautiful problem from Probability based on Positive factors

## Probability – AMC-10A, 2003- Problem 8

What is the probability that a randomly drawn positive factor of $60$ is less than $7$?

• $\frac{1}{3}$
• $\frac{1}{2}$
• $\frac{3}{4}$

### Key Concepts

Probability

Factors

combinatorics

But try the problem first…

Answer: $\frac{1}{2}$

Source

AMC-10A (2003) Problem 8

Pre College Mathematics

## Try with Hints

First hint

Now at first we find out the positive factors of $60$ are $1,2,3,4,5,6,10,12,15,20,30,60$.but the positive factors which are less than $7$ are $1,2,3,4,5,6$

Can you now finish the problem ……….

Second Hint

so we may say that any For a positive number $n$ which is not a perfect square, exactly half of the positive factors will be less than $\sqrt{n}$.here $60$ is not a perfect square and $\sqrt 60 \approx 7.746$.Therefore half of the positive factors will be less than $7$

can you finish the problem……..

Final Step

Therefore the required probability=$\frac{1}{2}$