# Tag: Number Theory

## Types of Numbers

Types of Numbers Natural Numbers The set of natural numbers is represented by the symbol N, and is defined as the set of counting numbers. That is, the set of natural numbers, N = {1, 2, 3, 4, 5,….}. Note, zero is not a natural number. The set of even and odd numbers are two…

## Highest Common Factor (H.C.F.)

Highest Common Factor (H.C.F.) The highest common factor (H.C.F.) of a group of numbers is the largest natural number which divides into each number exactly, that is, without leaving a remainder. Example What is the H.C.F. of the numbers 12 and 28?

## Lowest Common Multiple (L.C.M.)

Lowest Common Multiple (L.C.M.) The lowest common multiple (L.C.M.) of a group of numbers is the lowest number that can be divided by each number in the group, without leaving a remainder. Example What is the L.C.M. of the numbers 3, 5 and 8?

## The Identity of Operations

The Identity of Operations The identity of an operation is defined as an action which results in the number being manipulated, remaining unchanged. The identity for an addition and a subtraction is zero. If zero is added to or subtracted from a number, then the sum/difference obtained is that number. Example The identity for a…

## The Inverse of Operations

The Inverse of Operations Recall the identity of a number under addition is zero. The inverse of a number x under addition, is a number which when added to x results in zero being the sum. Example Recall the identity of a number under multiplication is one. The inverse of a number x under multiplication,…

## Associative Law

Associative Law The associative law addresses the grouping of numbers, and states that the sum/product obtained in an addition/multiplication is not dependent on how the numbers are grouped. That is for additions: (a + b) + c = a + (b + c) Example For multiplication: (a x b) x c = a x (b…

## Commutative Law

Commutative Law The commutative law addresses the order in which an operation is completed, and states that numbers can be swapped and the sum/product remains the same in an addition/multiplication. That is for additions: a + b = b + a Example For multiplication: a x b = b x a Example

## Distributive Law

Distributive Law The distributive law is summarised by the identity below: (a + b) x c = a x c + b x c Example