Yes.
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Quotient 0, remainder 805. Note that you will always get this pattern when you divide a smaller number by a larger one - i.e., the quotient will be zero, and the remainder will be the dividend.
The numerical value is the same as the quotient of the two positive equivalents but the sign is always negative.
No. When you divide a number by another number, let's say 26/4, you can't always get a perfect number. In this case, 6*4 is 24, and you have 2 "remainder", or 2 left over. The quotient is the whole answer, in this case 6 remainder 2. So the remainder is part of the quotient, but not the whole quotient itself.
The answer is always positive. If the signs are the same (positive by positive, negative by negative), then the quotient is always positive. If the signs are different (positive by negative, negative by positive), then the quotient is always negative.
Unless they are divided by themselves or one, they will always have a remainder.