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

helpppp Mar 30, 2020

#1**0 **

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.

tertre Mar 30, 2020

#2**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.

Mosspelt6 Mar 30, 2020