10.2. If 100 is divided by some unknown number, the remainder is 16, and if 200 is divided by the same number, the remainder is 4. Find this number.

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10.2. It is clear that the desired number is greater than 16. Moreover, the numbers $100-16=84$ and $200-4=196$ must be divisible by the desired number. Since $84=3 \cdot 4 \cdot 7$ and $196=2 \cdot 2 \cdot 7 \cdot 7$, it is easy to conclude that these numbers have only one common divisor greater than 16, namely 28. Answer: 28.