4. (10 points) A two-digit number multiplied by 109 results in a four-digit number, which can be divided by 23 with a quotient being a single digit. The largest two-digit number equals $\qquad$ .


【Analysis】According to the problem, this two-digit number is a multiple of 23, and to make the product of this two-digit number and 109 a four-digit number, the possible values for this two-digit number are: $23, 46, 69$, and the largest is 69.

【Solution】Solution: According to the analysis, this two-digit number is a multiple of 23, and to make the product of this two-digit number and 109 a four-digit number, the possible values for this two-digit number are: $23, 46, 69$. In summary, the largest two-digit number is 69, so the answer is: 69.