The factors of 14 are 1, 2, 7, and 14.
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
The greatest common divisor of 14 and 84 is 14.
Now, we divide both parts of the ratio by the GCD:
14 ÷ 14 = 1
84 ÷ 14 = 6
So the simplified ratio is $\boxed{1:6}$.