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IMAS 2023–2024 Junior Division — First Round Question 23

IMAS · IMAS 2023–2024 Junior Division — First Round

Question 23

A four-digit number is good if it is divisible by the product of the number formed of its first two digits and the number formed of its last two digits. For example, 1352 is a good number since $\frac{1352}{13\times52}=2$. What is the positive difference between the greatest and the second greatest good number?