1. (7p) Two natural numbers less than 200 have a greatest common divisor (GCD) of 28, and their product is 32928. Determine the two numbers.
1. $(a, b)=28$ results in $a=28 x$ and $b=28 y, (x, y)=1$ ..... (1p)
$a \cdot b=32928$, results in $28 x \cdot 28 y=32928$ ..... (1p)
Thus $x y=42$ ..... (2p)
Since $a, b<200$, it follows that $x, y \leq 7$. ..... (1p)
Therefore, the only solutions are $x=6, y=7$ and then $a=168$ and $b=$ ..... 196
(1p)
Or $x=7, y=6$ and then $a=196$ and $b=168$ ..... (1p)