Chewing gum does not take more than a few hours to decompose. It is not a biodegradable substance, but it still gets digested quickly by stomach acids.
Chewing gums contain sweeteners and flavoring agents along with a gum base. It also contains softeners and preservatives. However, the gum base is a synthetic substance. It takes longer to dissolve as the saliva has very little effect on it. When the chewing gum enters the stomach, acids and stomach enzymes begin to work on it and render it into a paste much like other foodstuff. The chewing gum along with other undigested matter is quickly passed to the intestines and ejected through the colon.