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Divisibility tests are algorithms that can quickly decide if one integer isdivisible by another. There are many tests but most are either of the trimmingor summing variety. Our goals are to present Zbikowski's family of trimmingtests as one test and to unify the trimming and summing tests. We do the latterby showing, first, that the most effective summing tests, due to Khare, can bederived directly from the Zbikowski's test and, second, that the best knownsumming tests - the binomial tests - can be derived from an adapted form ofZbikowski's tests. We introduce the notion of stacking, the claim that a sixyear old would always choose 10 pennies over a dime, and use only basicdivisibility properties to achieve our goals.

Divisibility Tests Unified: Stacking the Trimmings for Sums