【Analysis】The value of the fraction is an integer, which means the denominator is a divisor of the numerator. Prime numbers greater than 11, such as $13, 17, 19$, can only serve as the numerator of 1 to form a fraction with an integer value. Then, write down these numbers.

【Solution】Solution: According to the analysis, the maximum number of integers that can be formed from 22 numbers is:
$$
\frac{22}{11}, \frac{21}{3}, \frac{20}{10}, \frac{19}{1}, \frac{18}{9}, \frac{16}{8}, \frac{15}{5}, \frac{14}{7}, \frac{12}{6}, \frac{4}{2} \text{.}
$$

Therefore, the maximum number of fractions with integer values is 10.
The answer is: 10.
8. (3 points) Fill in the " $\square$ " below with natural numbers $1 \sim 22$ (each " $\square$ " can only contain one number), in the 11 fractions formed, the maximum number of fractions that can have integer values is $\qquad$