Remainders: Tips and hints

DEFINITIONIf \(x\) and \(y\) are positive integers, there exist unique integers \(q\) and \(r\), called the quotient and remainder, respectively, such that \(y =divisor*quotient+remainder= xq + r\) and \(0\leq{r}<x\).For example, when 15 is divided by 6, the quotient is 2 and the remainder is 3 since \(15 = 6*2 + 3\).

TIPS1. \(0\leq{r}<x\) means that remainder is a

non-negative integer and

always less than divisor.

2. When \(y\) is divided by \(x\) the remainder is 0 if \(y\) is a multiple of \(x\).

For example, 12 divided by 3 yields the remainder of 0 since 12 is a multiple of 3 and \(12=3*4+0\).3. When a smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller integer.

For example, 7 divided by 11 has the quotient 0 and the remainder 7 since \(7=11*0+7\)4. The possible remainders when positive integer \(y\) is divided by positive integer \(x\) can range from 0 to \(x-1\).

For example, possible remainders when positive integer \(y\) is divided by 5 can range from 0 (when y is a multiple of 5) to 4 (when y is one less than a multiple of 5)..

5. If a number is divided by 10, its remainder is the last digit of that number. If it is divided by 100 then the remainder is the last two digits and so on.

For example, 123 divided by 10 has the remainder 3 and 123 divided by 100 has the remainder of 23.Please share your Remainders tips below and get kudos point. Thank you.
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