445. Find all pairs of natural numbers whose sum is 288, and the greatest common divisor is 36.
$\triangle$ Let the required numbers be $a$ and $b$. Since their greatest common divisor is 36, then

$$
a=36 k, \quad b=36 n
$$

where $k$ and $n$ are coprime natural numbers. Then

$$
a+b=288, \quad 36 k+36 n=288, \quad k+n=8
$$

What are $k$ and $n$ from the last equation? They are either 7 and 1, or 5 and 3. From here we find $a$ and $b$.

Answer: 252, 36; 180, 108.