The dilution factor essentially tells you by what factor the concentration of the diluted solution decreased compared with the concentration of the initial solution.
A dilution is based on the principle that you can decrease the concentration of a solution by
- keeping the number of moles of solute constant
- increasing the volume of the solution
The dilution factor can thus be calculated by dividing the volume of the target solution, i.e. the diluted solution, by the volume of the initial solution, i.e. the concentrated solution.
#color(blue)(|bar(ul(color(white)(a/a)"D.F." = V_"diluted"/V_"concentrated"color(white)(a/a)|)))#
In your case, you are adding
The total volume of the diluted solution will be
#V_"diluted" = "100 mL" + "200 mL" = "300 mL"#
The dilution factor will thus be
#"D.F." = (300 color(red)(cancel(color(black)("mL"))))/(100color(red)(cancel(color(black)("mL")))) = 3#