How to divide it?

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 the real number field);

(2) Dividend = divisor × quotient+remainder;

Divider = (dividend-remainder) ÷ quotient;

Quotient = (dividend-remainder) divider;

Remainder = dividend-divisor × quotient.

(3) If the remainders of A and B divided by C are the same, then the difference between A and B can be divisible by C. For example, if the remainders of 17 and1divided by 3 are 2, then17-1can be divisible by 3.

(4) The sum of A and B divided by the remainder of C (except that 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. Note: When the sum of remainders is greater than the divisor, the remainders are equal to the sum of remainders and divided by the remainder of c ... For example, the remainders of 19 divided by 5 are 3 and 4 respectively, so the remainders of (23+ 19) divided by 5 are equal to the remainders of (3+4) divided by 5.

(5) The product of A and B divided by C is equal to the product of A and B divided by C (or the product divided by C). For example, 23, the remainder of 16 divided by 5 is 3 and 1 respectively, so the remainder of (23x16) divided by 5 is equal to. 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, 23, and the remainder of 19 divided by 5 is 3 and 4 respectively, then the remainder of (23× 19) divided by 5 is equal to that of (3×4) divided by 5.

Properties (4) and (5) can be extended to the case of multiple natural numbers.