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# help( basic probability)

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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
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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
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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