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Question

give an example in which remainder is greater than divisor

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Solution

The remainder can NEVER be greater than divisor
The quotient remainder theorem says:
Given any integer A, and a positive integer B, there exist unique integers Q and R such that
A= B * Q + R where 0 ≤ R < B
We can see that this comes directly from long division. When we divide A by B in long division, Q is the quotient and R is the remainder.
If we can write a number in this form then A mod B = R

This is because when we divide numbers, we always choose the quotient (the result of the division) to be the largest whole number of divisors possible to fit into the dividend (thing being divided). We find that when the divisor doesn’t exactly divide the dividend, conventionally, we set things up so the leftover falls short. Then, when it is appropriate to use fractions or decimals, one can put the remainder over the divisor, and the result is the mixed number,

(dividend) + (remainder/divisor).

For example, 50/3 is 16, with remainder of 2. Three 16’s give 48, and 2 more are needed to make 50. The mixed number form is just 16 2/3 (the remainder 2, divided by the divisor, 3).


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