There are several ways to describe variance. The first is to say some thing has many different variations, in which case "vary in" is appropriate:
Apples vary in size, color, taste, and texture.
In this case it sounds more like you want to say the variance depends on some other factors. Here "vary with" is appropriate:
The size of the stadium crowds varies with the weather.
Singular or plural doesn't really matter:
What people eat varies with the available options.
Also, it is correct to use the definite article "the" before the factors, if you've already described them.
The decision will vary with the given factors.
However all that being said, the more "natural" way to say this would be:
The decision depends on the various given factors.