This is a common operation in Number Theory, especially in relation to Euclid's Algorism.
If, when dividing two numbers, complete division does not occur then usually the operation stops at a value less than the dividend and the resulting difference is described as the remainder.
Example : 88 ÷ 7 = 12 with remainder 4. (12 x 7 = 84)
A negative remainder is when the division stops at a value greater than the dividend. Normally this is the value immediately greater than the dividend.
Example : 88 ÷ 7 = 13 with remainder -3 (13 x 7 = 91)
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This means you divide a number and whatever you have left over is your remainder,
A remainder can be any non-negative number that is less than the divisor. If the remainder is bigger than the divisor, the divisor can go into it another one (or more) times until the remainder is brought into that range.
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Do the division and if the remainder is 0 then the number is divisible by the something and if not it isn't.
There is no need to find the square root of a negative number for sqrt(0.6)!