Divisibility rules are incredibly useful tools in number theory. They provide quick ways to determine if a number is divisible by another without performing long divisions. For example, a number is divisible by 2 if its last digit is 0, 2, 4, 6, or 8. To check divisibility by 3, sum the digits of the number and assess if the result is divisible by 3. Divisibility rules exist for other numbers as well, such as 4, 5, 6, 9, and 10. These rules can save us a lot of time and effort when solving problems involving divisibility.