Problem 735

【Analysis】According to the problem, there are 55 apples, 114 cookies, and 83 chocolates. After distributing them evenly, there are 3 apples, 10 cookies, and 5 chocolates left. Therefore, a total of 52 apples, 104 cookies, and 78 chocolates were distributed. Then, we need to find the greatest common divisor (GCD) of these three numbers to get the answer.

【Solution】Solution: $55-3=52, 114-10=104, 83-5=78$,
$$\begin{array}{l} 52=2 \times 2 \times 13, \\ 104=2 \times 2 \times 2 \times 13, \\ 78=2 \times 3 \times 13, \end{array}$$

Therefore, the greatest common divisor of $52$, $104$, and $78$ is $2 \times 13=26$.
Answer: The class has at most 26 children.
The answer is: 26.