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

 Mar 30, 2020
 #1
avatar+4599 
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60 is 2^2*3*5 and it has 3*2*2=12 factors.

 

1, 2, 3, 4, 5 and 6 are all less than seven...

 

6/12=1/2 is the probability that a randomly drawn positive integer factor of 60 is less than 7.

 Mar 30, 2020
 #2
avatar+34 
0

\(\)For a positive number N which is not a perfect square, exactly half of the positive factors will be less than \(\sqrt{n}\). Since 60 is not a perfect square, half of the positive factors of 60 will be less than \(\sqrt{60}\), or about 7.746. 

Clearly, there are no positive factors of  between 7 and \(\sqrt{60}\).

Therefore half of the positive factors will be less than 7.

So the answer is 1/2.

 Mar 30, 2020

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