The remainder refers to the undivided part of the dividend in integer division, and the range of the remainder is an integer between 0 and divisor, which is a mathematical term. In the division of integers, there are only two situations: divisible and non-divisible. When it is not divisible, a remainder is generated, and the remainder operation: amodb=c(b is not 0) means that the remainder obtained by dividing integer A by integer B is C.
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. In the division of integers, there are only two situations: divisible and non-divisible. When it is not divisible, it will produce a remainder, so the remainder problem is very important in primary school mathematics.
The remainder has the following important properties (A, B and C are all natural numbers):
1, 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).
2, dividend = divisor × quotient+remainder; Divider = (dividend-remainder) ÷ quotient; Quotient = (dividend-remainder) divider; Remainder = dividend-divisor × quotient.
3. If the remainder of a and b divided by c is the same, then the difference between a and b can be divisible by c. For example, the remainder of 17 and1divided by 3 is 2, then17-1can be divisible by 3.
4. The sum of A and B divided by the remainder of C (except when A and B divided by C have no remainder) is respectively equal to the sum of the remainder of A and B divided by C (or the remainder of this sum divided by C). For example, 23, the remainder of 16 divided by 5 is 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. ..