# Division Algorithm

**Theorem**(Division Algorithm)

Let *a* and *b* be integers with *b > 0*. Then there exist unique integers *q* and *r* with the property that *a = b*q + r*, where *0 ≤ r < b*.

**Remark**

*a/b*,

*division(a,b) =* *:* , is some real number.

For, *a = b*q + r*,

*a* is dividend,

*b* is divisor,

*q* is quotient,

*r* is remainder.

**Example**

let *a = 21, b = 4*,

then *21 = 4*5 + 1*, here *q = 5* and *r = 1*.

If *b = 3*,

then *21 = 3*7 + 0*, here *q = 7* and *r = 0*.

Whenever *r = 0*, we say,

*b* is divisor of *a* or,

*a* is multiple of *b* or,

b divides a.

*a* is divisible by *b*.