A method for verifying the correctness of an arithmetical operation on natural numbers, based on the same principle as casting out nines. The methods of sevens takes advantage of the fact that the residue (mod 7) of a sum (or product) must be equal to the sum (or product) of the residues of the summands (or factors). For example, the correct sum 45 + 34 = 79 corresponds to a correct sum of residues mod 7 3 + 6 = 2, where, on the right-hand side, 9 has been replaced by its residue 2 (mod 7).

casting out nines | divisibility tests