Basic number theory, including prime numbers and divisibility rules

Number theory is a branch of mathematics that deals with the properties and relationships of numbers. In this tutorial, we will cover the basics of number theory, including prime numbers and divisibility rules.

A prime number is a whole number greater than 1 that is only divisible by 1 and itself. For example, 2, 3, 5, and 7 are all prime numbers, because they cannot be divided evenly by any other number except 1 and themselves. Prime numbers are important in number theory because they are the building blocks of all other numbers.

Divisibility rules are a set of rules that tell us whether a given number is divisible by another number without actually having to perform the division. These rules are based on the properties of prime numbers and can be used to quickly determine whether a number is divisible by 2, 3, 4, 5, 6, 9, or 10. For example, to determine whether a number is divisible by 2, we only need to check the last digit of the number. If the last digit is even, the number is divisible by 2.

In this tutorial, we will go over these concepts in more detail and explore the properties and applications of prime numbers and divisibility rules. We will also learn about more advanced topics in number theory, such as modular arithmetic and the Euclidean algorithm. By the end of this tutorial, you should have a good understanding of the basics of number theory and be able to apply these concepts to solve problems involving prime numbers and divisibility.