8.4. When a certain number is divided by 13 and 15 with a remainder, the same incomplete quotients are obtained. Find the largest such number.
Answer: 90. Suppose the number a satisfies the condition of the problem. Then the equalities $a=13 d+b=15 d+c$ hold, where $d$ is the quotient from the condition of the problem. From this, $2 d=b-c \leq 12$, i.e., $d \leq 6$, and the remainder $b$ from dividing the number by 13 is no more than 12. For $d=6$ and $b=12$, we obtain the desired largest number 90. Verification: $90=13 \cdot 6+12, 90=15 \cdot 6+0$.

Comment. The number 90 is provided with verification of this number without justification of its maximality - 1 point. The number 90 is provided with justification of the estimate without verification of this number - 5 points.