100:685

To simplify the ratio \(100:685\), you can divide both numbers by their greatest common divisor (GCD).

1. Find the GCD of 100 and 685. The factors of 100 are \(1, 2, 4, 5, 10, 20, 25, 50, 100\), and the factors of 685 are \(1, 5, 137, 685\). The GCD is \(5\).

2. Divide both numbers by the GCD:

\[ \frac{100}{5} : \frac{685}{5} = 20 : 137 \]

Thus, the simplified form of the ratio \(100:685\) is \(20:137\).