Question

随机选取 $60$ 的一个正因数，该因数小于 $7$ 的概率是多少？

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

$\dfrac{1}{10}$

$\dfrac{1}{6}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

$60=2^2\cdot3\cdot5$ ，所以它有 $(2{+}1)(1{+}1)(1{+}1)=12$ 个因数。

$60=2^2\cdot3\cdot5$ has $(2{+}1)(1{+}1)(1{+}1)=12$ factors

数出从 $1$ 到 $6$ 的因数。

Count the factors from $1$ through $6$

$60$ 的 $12$ 个正因数为 $1,2,3,4,5,6$ ，以及 $10,12,15,20,30,60$ 。

其中小于 $7$ 的有六个： $1,2,3,4,5,6$ ，所以概率为 $\dfrac{6}{12}=\dfrac12$ 。

所以正确答案是 E。

The number $60$ has $12$ positive factors: $1,2,3,4,5,6,$ $10,12,15,20,30,60.$

Six of them are less than $7,$ namely $1,2,3,4,5,6,$ so the probability is $\dfrac{6}{12}=\dfrac12.$

Thus, the correct answer is E.