In the division of integers, there are only two situations: divisible and non-divisible. When it is not divisible, a remainder is generated. The remainder operation: a mod b = c(b is not 0) means that the remainder obtained by dividing the integer a by the integer b is c, for example, 7 ÷ 3 = 2 1.
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
Extended data:
Dividend = Divider× Quotient+Remainder;
Divider = (dividend-remainder) ÷ quotient;
Quotient = (dividend-remainder) divider;
Remainder = dividend-divisor × quotient.
Example: The sum of dividend, divisor, quotient and remainder is 2 143, the known quotient is 33 and the remainder is 52. Find dividend and divisor.
Solution: Because dividend = divisor× quotient+remainder = divisor× 33+52,
Dividend =2 143- divisor-quotient-remainder =2 143- divisor -33-52=2058- divisor,
So divisor ×33+52=2058- divisor, so divisor =(2058-52)÷34=59,
Dividend =2058-59= 1999.
A: The dividend is 1999 and the divisor is 59.
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