Using the digits from 1 to 5 and a multiplication sign $\times$, Clara forms the product of 2 numbers, with the sign $\times$ between them. How should Clara place the cards to obtain the largest possible product?
![](https://cdn.mathpix.com/cropped/2024_05_01_dbce7bc2a200e234c3e2g-05.jpg?height=186&width=198&top_left_y=568&top_left_x=1473)
Observe that we obtain the largest possible result if one of the numbers starts with the digit 5 and the other with 4. Let's look at the possibilities that give the largest product:

- one of the factors has 1 digit:

$5321 \times 4=21284 ; 4321 \times 5=21605$

- one of the factors has 2 digits:

$532 \times 41=21812 ； 531 \times 42=22302 ； 521 \times 43=22403$

It's good to use a calculator.

$432 \times 51=22032 ； 431 \times 52=22412 ； 421 \times 53=22313$.

Therefore, the best result is $431 \times 52=22412$.