2. (10 points) Divide 120 boys and 140 girls into several groups, requiring that the number of boys in each group is the same, and the number of girls in each group is also the same, then the maximum number of groups that can be formed is $\qquad$ groups.
【Analysis】To make the number of boys and girls in each group the same, we only need to find the greatest common divisor of 120 and 140, which will give us the solution.

【Solution】Solution: $120=2 \times 2 \times 2 \times 3 \times 5$,
$$
140=2 \times 2 \times 5 \times 7,
$$

Therefore, the greatest common divisor of 120 and 140 is $2 \times 2 \times 5=20$,
Answer: The maximum number of groups that can be formed is 20.
So the answer is: 20.