The remainder refers to the undivided part of the dividend in integer division, and its value range is 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.
Extended data:
Remainder operation:
A mod b = c means that the remainder obtained by dividing the integer a by the integer b is C.
The formula for calculating the remainder: c = a-? a/b？ * b
Among them, it is a downward integer operator, and the downward integer operation is called Floor, which is represented by mathematical symbols.
Example:? 3.476 ? =3,? 6.7546? =6,? -3. 14 159? = -4
For example, 7 mod 3 = 7-? 7/3? *3=7-2*3= 1
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 3+ 1=4. 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.