There are, as I’m sure you know, a lot of numbers, infinitely many as it happens. Because of this mathematicians need a way to classify numbers, a way to group then and tell them apart from each other. We are going to take look at the different groups of numbers that exist.

### Natural Numbers

Natural numbers – or the *counting numbers* – are probably the first type of numbers you will have come across. The Natural numbers are whole numbers greater than zero. These numbers are **1, 2, 3, 4, …**, numbers that you can physically count. The Natural Numbers do not include negative values. For these we need another group.

*Note: Some people include zero as a Natural Number, if unsure it is best to check with your teachers whether they do or not.*

### Integers

Integers are whole numbers, both negative and positive, including zero. These numbers are **…, -3, -2, -1, 0, 1, 2, 3, …**. Positive integers are integers greater than zero, and negative integers, not surprisingly, are integers less than zero.

### Rational Numbers

Rational number are numbers that can be written as a fraction where both the numerator and denominator are integers. This means that both the top and bottom of the fraction are whole numbers. Examples of these would be and .

### Irrational Numbers

Irrational Numbers are numbers that **can’t** be written as fractions, examples of these are ones such as and . If we try to write these numbers as decimals they go on forever, with no recurring digits.

### Square Numbers

Square Numbers are integers that can be written as the square of some other integers, ie. a product of an integer multiplied by itself. Examples of these are **4, (2×2)** and **81, (9×9)**. Square Numbers can also be written in the form . This notation means 5 squared, which is 25.

### Surds

Surds are numbers left in the form , where n is a positive integer that is not a square number. For more in-depth information about Surds be sure read our article Surds

### Prime Numbers

Prime numbers are numbers greater than 1 that can only be divided by themselves and 1 to give an integer answer. Example of these are **2, 3, 5, 7, 11, 13, 17, …**. Note that 2 is the first and only even prime number.

*Note: Some courses class the number 1 as a prime number, if unsure it is again best to check with your teacher.*

### Real Numbers

Real numbers are all the numbers that you have ever come across, all of the rational and irrational numbers. All of these real numbers can be written in a finite or infinite decimal form, such as … and .