532. A six-digit number starts with the digit 2. If this digit is moved to the last place, the number increases by 3 times. What is this number?
$\triangle$ Let's solve the problem in two ways.

1) Restore the record:

![](https://cdn.mathpix.com/cropped/2024_05_21_475fdfbb473422773b9eg-109.jpg?height=137&width=165&top_left_y=1182&top_left_x=954)

where the five-digit numbers denoted by asterisks in the first multiplier and in the product coincide. We sequentially obtain:

![](https://cdn.mathpix.com/cropped/2024_05_21_475fdfbb473422773b9eg-109.jpg?height=148&width=1132&top_left_y=1408&top_left_x=468)

(Here, we first find the digit 4 in the first multiplier and then place it in the corresponding position in the product; we first find the digit 1 in the first multiplier and then place it in the product, and so on.)

We get the number 285714.

2) Let the desired number be $200000 + x$, where $x$ is the number formed by the last five digits. Then

$$
(200000 + x) \cdot 3 = 10x + 2
$$

From this,

$$
x = 85714, \quad 200000 + x = 285714
$$

Answer: 285714.