# 8. Variant 1

Petya wrote down all positive numbers that divide some natural number $N$. It turned out that the sum of the two largest written numbers is 3333. Find all such $N$. If there are several numbers, write their sum in the answer.
Answer: 2222.

Solution: Note that one of the listed numbers will be equal to $N$. Since the sum of the two largest listed numbers is odd, these numbers have different parity. This means that the number 2 is a divisor of $N$, so the second number is $N / 2$. According to the condition, $N + N / 2 = 3333$. Therefore, $N = 2222$.

## Variant 2

Petya listed all positive numbers that divide some natural number $N$ on the board. It turned out that the sum of the two largest listed numbers is 3021. Find all such $N$. If there are several numbers, write their sum in the answer.

Answer: 2014.

## Variant 3

Petya listed all positive numbers that divide some natural number $N$ on the board. It turned out that the sum of the two largest listed numbers is 6663. Find all such $N$. If there are several numbers, write their sum in the answer.

Answer: 4442.

## Variant 4

Petya listed all positive numbers that divide some natural number $N$ on the board. It turned out that the sum of the two largest listed numbers is 3201. Find all such $N$. If there are several numbers, write their sum in the answer.

Answer: 2134.

## Variant 5

Petya listed all positive numbers that divide some natural number $N$ on the board. It turned out that the sum of the two largest listed numbers is 2301. Find all such $N$. If there are several numbers, write their sum in the answer.

Answer: 1534.