Division : Division is the mathematical operation that divides objects equally into groups. More generally $x\div y$ is defined as the number that if multiplied by $y$ equals $x.$

Remainder : In the division of a whole number $x$ by a natural number $y$ the remainder is the unique whole number $r$ with $0\leq r\lt y$ with $x=m\cdot y+r$ for some whole number $m.$ The remainder is the number of leftover wholes in the division. For example the remainder of the division of 14 by 3 is 2 as $14=4\cdot 3+2.$ Remainders are fundamental for the concept of congruence modulo $y$ in number theory.

Standard algorithm : By standard algorithm we refer to any one of the algorithms that are commonly taught at school to add, subtract, multiply or divide multi-digit numbers such as long division and partial products multiplication.