Problem 5. The product of a two-digit and a three-digit natural number is written in decimal notation using only the digit 2. Determine those numbers.
Solution. The product of a two-digit and a three-digit number is greater than $10 \cdot 100=1000$, and less than $100 \cdot 1000=10000$, so the product is one of the numbers 2222 or 22222. If the product is the number $2222=2 \cdot 11 \cdot 101$, then the possible cases are $11 \cdot 202$ or 22$\cdot$101.(5) If the product is the number $22222=2 \cdot 41 \cdot 271$, then the possible cases are $82 \cdot 271$ or $41 \cdot 542$.

## VIII Department