# 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) = ${\displaystyle x}$: ${\displaystyle x\in Z}$, ${\displaystyle x}$ 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.