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negative number divided by positive number, what would be remainder?

I've read these answers linked above, but I don't feel I'm answered enough. $$-27 = \underbrace{-6}_q\cdot \underbrace{5}_d + \underbrace{3}_r$$ They say this, but I don't think I can use it later when I need to divide some large minus number with another large positive number, such as -777777 with 439. The traditional positive number division is easy enough that no matter how young you are, even grammar school students could solve it with enough time given. I was wondering if there's any that kind of easy method to get the quotient and remainder from the minus numbers divided by the positive numbers.

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Try this, First dived the number by asumming the number to be positive ( in your example 777777) then remainder when we divide it by 5 is 2 so when -777777 is divided by 5 remainder would be -2 but the tradition in mathematics is to always put remainder positive so just add 5 to -2 so the remainder will be 3.

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