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Try this beautiful problem from Probability based on Positive factors

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

- \(\frac{1}{3}\)
- \(\frac{1}{2}\)
- \(\frac{3}{4}\)

Probability

Factors

combinatorics

But try the problem first...

Answer: \(\frac{1}{2}\)

Source

Suggested Reading

AMC-10A (2003) Problem 8

Pre College Mathematics

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=\(\frac{1}{2}\)

- https://www.cheenta.com/area-of-triangle-problem-amc-10a-2009-problem-10/
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