# Divisibility Rule for 18: The Ultimate Guide

If you’ve ever struggled with finding out if a number is divisible by 18, you’re not alone. This can be a tricky task, especially when dealing with larger numbers. However, with the help of the divisibility rule for 18, you can quickly determine whether a number is divisible by 18 or not. In this article, we’ll discuss the mathematics behind this rule, how to apply it, and why it’s important.

## What is the Divisibility Rule for 18?

The divisibility rule for 18 states that a number is divisible by 18 if and only if it is divisible by both 9 and 2. To check if a number is divisible by 9, you simply add up all its digits. If the sum is divisible by 9, then the original number is also divisible by 9. To check if a number is divisible by 2, you just need to check if its last digit is even or odd.

## How to Apply the Divisibility Rule for 18?

Let’s take the number 2,106 as an example. To check if it is divisible by 18, we first need to check if it is divisible by 9. To do this, we add up its digits:

2 + 1 + 0 + 6 = 9

Since 9 is divisible by 9, we move on to the next step, which is to check if the number is divisible by 2. We can do this by looking at its last digit, which is 6. Since 6 is even, the number 2,106 is also divisible by 2. Therefore, it is divisible by 18.

## Why is the Divisibility Rule for 18 Important?

The divisibility rule for 18 is essential in many different areas of mathematics, such as algebra, calculus, and number theory. It’s also a useful tool in everyday life, especially when dealing with fractions or decimals. Being able to quickly determine whether a number is divisible by 18 can save you time and prevent errors.

## The Mathematics behind the Divisibility Rule for 18

To understand why the divisibility rule for 18 works, we need to look at the prime factorization of the number 18.

18 = 2 * 3 * 3

If a number is divisible by 18, it must also be divisible by all its factors, which are 2, 3, and 3. We already know that a number is divisible by 2 if its last digit is even, so we just need to focus on the factor 3.

The divisibility rule for 9 states that if the sum of a number’s digits is divisible by 9, then the number itself is divisible by 9. Since 9 is a factor of 18, we can use this rule to determine whether a number is divisible by 18.

Let’s take the number 2,340 as an example.

2 + 3 + 4 + 0 = 9

Since the sum of the digits is divisible by 9, we know that the number is divisible by 9. We can also see that the last digit is even, so the number is divisible by 2. Therefore, it is divisible by 18.

## Tips for Using the Divisibility Rule for 18

Here are some tips to keep in mind when using the divisibility rule for 18:

• Always check if the number is divisible by 9 first, since this is the more restrictive condition.
• If a number is not divisible by 9, then it cannot be divisible by 18.
• If the last digit of a number is odd, then it cannot be divisible by 2 or 18.
• When adding up the digits to check for divisibility by 9, you can continue adding until you get a single digit. For example, 1 + 2 + 3 + 4 + 5 = 15, and 1 + 5 = 6, so we know that the original number is divisible by 9 if and only if it is divisible by 6.

## Examples of Divisibility Rule for 18

Let’s take a look at some examples to further illustrate the divisibility rule for 18.

Example 1: Is 3,024 divisible by 18?

First, we check if it is divisible by 9:

3 + 0 + 2 + 4 = 9

Since the sum of the digits is divisible by 9, we move on to the next step and check if it is divisible by 2. The last digit is even, so we know that 3,024 is divisible by 2. Therefore, it is also divisible by 18.

Example 2: Is 8,691 divisible by 18?

First, we check if it is divisible by 9:

8 + 6 + 9 + 1 = 24

We can keep adding to get a single digit:

2 + 4 = 6

Since 6 is not divisible by 9, we know that 8,691 is not divisible by 9 or 18.

## Conclusion

The divisibility rule for 18 is a useful tool for quickly determining whether a number is divisible by 18 or not. By checking if a number is divisible by both 9 and 2, we can save time and prevent errors in many different areas of mathematics and everyday life. Remember to always check if a number is divisible by 9 first, and keep in mind the tips and examples provided in this article to become proficient in using this rule.

## FAQs

What is the divisibility rule for 18?

The divisibility rule for 18 states that a number is divisible by 18 if and only if it is divisible by both 9 and 2.

Why is the divisibility rule for 18 important?

The divisibility rule for 18 is important in many different areas of mathematics, such as algebra, calculus, and number theory, and is also useful in everyday life.

How do you check if a number is divisible by 9?

To check if a number is divisible by 9, add up all its digits. If the sum is divisible by 9, then the original number is also divisible by 9.

What should you check first when using the divisibility rule for 18?

Always check if the number is divisible by 9 first, since this is the more restrictive condition.

Can you use the divisibility rule for 18 to check if a number is divisible by 3?

No, you cannot use the divisibility rule for 18 to check if a number is divisible by 3, since 18 is not a factor of 3. Instead, you can use the divisibility rule for 3, which states that a number is divisible by 3 if and only if the sum of its digits is divisible by 3.