__This is an insight from lesson [AR1] Arithmetic, Number Theory __

Number theory is a branch of mathematics that is devoted to studying **natural numbers**. These are numbers that are most familiar to you, starting with {1,2,3,...}, and reaching until infinity. As you can imagine, these numbers are quite fundamental for all of mathematics. Therefore **Number Theory **is also called the **queen of mathematics**.

*If you wonder who the king of mathematics is, you have heard of him;** Leonhard Euler**. He created a mathematical formula that is all over the place in mathematics, physics and engineering. Look it up if you're interested. *

When you look at all types of numbers in the illustration above, you see that next to natural numbers, there are **whole numbers**. This set of numbers is much the same as the set of natural numbers, however **zero **is included {0,1,2,...}. Take it another step broader and you will find **integers**, which are whole numbers that are either **positive**, **negative**, or exactly **zero**. Integer is a word that you will read a lot during your GMAT practice and during the exam. Examples of integers are the numbers 2 and 3, but √25 is also an integer, as you can **express it as a number**, in this case the number 5. When decimals are included, we speak of** rational numbers**.

Less common forms of numbers are termed **irrational numbers**, which are numbers that **cannot be represented as a integer or decimal/fraction**. A well-known example is '**Pi**', which is used to circumscribe a circle and has a value of 3.14(...). The digits after the decimal point extend infinitely without a pattern, so strictly it is not possible to express Pi as a decimal, hence it is an irrational number.

Now do you want to dive deeper into the concept of number theory and understand these quotes?

All prime numbers except 2 and 5 end with either the digits 1, 3, 7 or 9.

When you encounter parentheses next to each other, it means you have to multiply them.

Then check out the preview of the course ** here**.

*Feel free to reach out, we're here to help.*