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The remainder of a division of two integers is the integer such that , where is the quotient; in other words, is the part of that is not divisible by . If , and , for example, the division would have remainder , since (notice that the quotient, in this case, is one). If is a divisor of , the remainder is said to be zero.
It is important to notice that the remainder is most useful when an integer quotient is desired, as we can always say that for any real number (in the example provided earlier, ).