Examples of Divisibility by 9

Oct 13, 2025 by windailys.com 42 views

Introduction

In mathematics, divisibility is a fundamental concept that deals with the ability of a number to be divided by another number without leaving a remainder. One of the most interesting and useful divisibility rules is the rule for divisibility by 9. In this article, we will explore the rules and examples of divisibility by 9, and answer some questions related to this topic.

What is Divisibility by 9?

Divisibility by 9 is a rule that states that a number is divisible by 9 if the sum of its digits is also divisible by 9. This means that if we take the individual digits of a number and add them together, the result should be a multiple of 9 for the original number to be divisible by 9.

Examples of Divisibility by 9

Let's consider some examples to illustrate this rule.

Example 1: The number 918 is divisible by 9 because the sum of its digits (9 + 1 + 8 = 18) is a multiple of 9.
Example 2: The number 279 is divisible by 9 because the sum of its digits (2 + 7 + 9 = 18) is a multiple of 9.
Example 3: The number 369 is divisible by 9 because the sum of its digits (3 + 6 + 9 = 18) is a multiple of 9.

Which Numbers are Divisible by 9?

Now, let's answer the question: which numbers are divisible by 9?

Answer: The numbers 818, 962, and 265 are not divisible by 9.

However, if we apply the divisibility rule for 9, we can see that the sum of the digits for each of these numbers is not a multiple of 9.

818: 8 + 1 + 8 = 17 (not divisible by 9)
962: 9 + 6 + 2 = 17 (not divisible by 9)
265: 2 + 6 + 5 = 13 (not divisible by 9)

Therefore, none of the numbers 818, 962, and 265 are divisible by 9.

Conclusion

Introduction

In our previous article, we explored the rules and examples of divisibility by 9. In this article, we will provide a Q&A guide to help you better understand the concept of divisibility by 9. Whether you're a student, a teacher, or simply someone who wants to learn more about mathematics, this guide is for you.

Q: What is the divisibility rule for 9?

A: The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is also divisible by 9.

Q: How do I apply the divisibility rule for 9?

A: To apply the divisibility rule for 9, simply add up the individual digits of a number and check if the result is a multiple of 9.

Q: What are some examples of numbers that are divisible by 9?

A: Here are some examples of numbers that are divisible by 9:

Example 1: The number 918 is divisible by 9 because the sum of its digits (9 + 1 + 8 = 18) is a multiple of 9.
Example 2: The number 279 is divisible by 9 because the sum of its digits (2 + 7 + 9 = 18) is a multiple of 9.
Example 3: The number 369 is divisible by 9 because the sum of its digits (3 + 6 + 9 = 18) is a multiple of 9.

Q: What are some examples of numbers that are not divisible by 9?

A: Here are some examples of numbers that are not divisible by 9:

Example 1: The number 818 is not divisible by 9 because the sum of its digits (8 + 1 + 8 = 17) is not a multiple of 9.
Example 2: The number 962 is not divisible by 9 because the sum of its digits (9 + 6 + 2 = 17) is not a multiple of 9.
Example 3: The number 265 is not divisible by 9 because the sum of its digits (2 + 6 + 5 = 13) is not a multiple of 9.

Q: Why is the divisibility rule for 9 useful?

A: The divisibility rule for 9 is useful because it helps us quickly identify whether a number can be divided by 9 without leaving a remainder. This can be especially helpful in mathematics and other fields where divisibility is an important concept.

Q: Can I use the divisibility rule for 9 to find the remainder of a division problem?

A: Yes, you can use the divisibility rule for 9 to find the remainder of a division problem. If a number is not divisible by 9, you can use the rule to find the remainder by subtracting the sum of the digits from the original number.

Q: Are there any other divisibility rules that I should know about?

A: Yes, there are several other divisibility rules that you should know about, including the rules for divisibility by 2, 3, 4, 5, 6, 7, 8, 10, and 11. Each of these rules has its own unique characteristics and can be used to help you solve division problems.

Conclusion

In conclusion, the divisibility rule for 9 is a useful tool that can help you quickly identify whether a number can be divided by 9 without leaving a remainder. By applying this rule, you can solve division problems and find the remainder of a division problem. We hope this Q&A guide has provided you with a better understanding of the concept of divisibility by 9 and has helped you answer some of the most frequently asked questions about this topic.