Task 3. Determine the largest five-digit number such that the product of its digits is 2520?
Solution. We have $2520=2^{3} \cdot 3^{2} \cdot 5 \cdot 7$. If 1 is among the digits of the desired number, then the product of the remaining digits does not change. Therefore, the largest possible number with the desired property will be obtained if we find four of the largest single-digit numbers from the factors. These are the numbers $3^{2}=9, 2^{3}=8, 7$ and 5, and the largest five-digit number that satisfies the condition of the problem is 98751.