Solving problems by remainder division refers to the use of division in integer division where the dividend is not divided, and the range of remainder value is between 0 and dividend (excluding dividend) as an application problem.

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. ..