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Remainder, a mathematical term. In the division of integers, there are only two situations: divisible and non-divisible. The remainder can't be generated in time. The remainder operation amodb=c(b is not 0) means that the remainder obtained by dividing integer A by integer B is c, for example, 7÷3=2… 1, and more professional symbols can also be written as 7÷3=2 and 1/3, or 7mod3= 1.
The remainder refers to the undivided part of the dividend in integer division (taking positive numbers as an example here), and the value range of the remainder is an integer between 0 and divisor (excluding divisor). For example, if 27 is divided by 6, the quotient is 4 and the remainder is 3. If a number is divided by another number, if it is smaller than another number, the quotient is 0 and the remainder is itself. For example: 1 divided by 2, the quotient is 0, and the remainder is1; When 2 is divided by 3, the quotient is 0 and the remainder is 2.
The remainder has the following important properties (A, B and C are all natural numbers): the absolute value of the difference between the remainder and the divisor is less than the absolute value of the divisor (applicable to real number fields); Dividend = Divider× Quotient+Remainder; Divider = (dividend-remainder) ÷ quotient; Quotient = (dividend-remainder) divider; Remainder = dividend-divisor × quotient. If the remainder of a and b divided by c is the same, then the difference between a and b can be evenly divided by C.
For example, if the remainder of 17 and 1 1 divided by 3 is 2, then17-1can be divisible by 3. The sum of A and B divided by the remainder of C (except when A and B divided by C have no remainder) is equal to the sum of the remainder of A and B divided by C respectively (or the remainder of this sum divided by C). For example, the remainder of 23 and 16 divided by 5 are 3 and 1 respectively, so the remainder of (23+ 16) divided by 5 is equal to 3+ 1=4. Note: When the sum of the remainder is greater than the divisor, the remainder is equal to the sum of the remainder and divided by the remainder of C. ..
For example, 23, the remainder of 19 divided by 5 is 3 and 4 respectively, so the remainder of (23+ 19) divided by 5 is equal to the remainder of (3+4) divided by 5. The remainder of the product of a and b divided by c is respectively equal to the remainder of the product of a and b divided by c (or the remainder of this product divided by c). For example, the remainder of 23 16 divided by 5 is 3 and 1 respectively, so the remainder of (23× 16) divided by 5 is equal to 3× 1=3. Note: when the product of the remainder is greater than the divisor, the remainder is equal to the product of the remainder divided by the remainder of C.
For example, if 23, 19 divides by 5 and the remainder is 3 and 4 respectively, then the remainder of (23× 19) divided by 5 is equal to the remainder of (3×4) divided by 5. These properties can be extended to the case of multiple natural numbers.