Types of Numbers

Common types of numbers found in Arithmetic.

Integer

any whole number including 0 such as 1, 2, or 3. $\frac{1}{2}$ is not a integer. $0.333\bar{3}$ is not an integer. $\frac{6}{3}$ is an integer even though it is a fraction because it reduces to 2 which is an integer. Negative whole numbers are also integers. The symbol for integers in mathematics is $\mathbb{Z}$ named after the German word 'zahlen.'

Even Number

Any number, $n$, that can be expressed as a multiple of 2. Now, 0 is an even number because $0 = 2 \cdot 0$. Negative numbers which are multiples of two are also even numbers.

Odd Number

an integer not evenly divisible by 2. 3 and 5 are odd numbers. Tecnically, an odd number is any number, $n$, that can be expressed as a multiple of two plus 1.

Prime Number

a positive integer that is evenly divisible only by 1 and itself. 2 is the first prime number. 2 is also the only even prime number. 7 is also a prime number.

Composite Number

a positive number that is evenly divisible by itself, 1, and another number. 2 is not a composite number because it is only divisible by itself and 1. At least three distinct positive integers must evenly divide a number that is to be called composite. 4 is the first composite number because it is evenly divisible by three integers, 4, 2, and 1. However, 5 is not composite. 6 is composite.

reciprocal

1 divided by the number. The reciprocal of 2 is $\frac{1}{2}$. </dl>