As we all know, arithmetic is a fundamental part of mathematics. It involves the study of numbers and their properties. One of the most important concepts in arithmetic is divisibility. Divisibility refers to the property of one number being able to divide another number without leaving a remainder. In this article, we will discuss the divisibility rule for the number 24.

## The Divisibility Rule for 24

To determine if a number is divisible by 24, we need to follow a few simple steps. Let’s take the number 768 as an example:

- First, we need to check if the number is divisible by 8. To do this, we look at the last three digits of the number. If they are divisible by 8, then the entire number is divisible by 8. In our example, the last three digits are 768, which is divisible by 8 since 768/8=96.
- Next, we need to check if the number is divisible by 3. To do this, we need to add up all the digits of the number. If the sum is divisible by 3, then the entire number is divisible by 3. In our example, the digits of 768 add up to 21, which is divisible by 3 since 21/3=7.
- If the number passes both the tests above, then it is divisible by 24. In our example, 768 is divisible by 24 since it is divisible by both 8 and 3.

## Why does the Divisibility Rule for 24 work?

The divisibility rule for 24 works because 24 is divisible by both 8 and 3. By checking if a number is divisible by 8 and 3, we can determine if it is also divisible by 24. This rule can be extended to other multiples of 24, such as 48, 72, and 96.

## Advantages of Knowing the Divisibility Rule for 24

Knowing the divisibility rule for 24 can be useful in many situations. For example, it can help us quickly determine if a number is divisible by 24 without having to perform long division. This can be particularly useful when dealing with large numbers.

Additionally, the divisibility rule for 24 can help us in problem-solving situations. For example, if we need to divide a large number by 24 and we know it is divisible by 8 and 3, we can simply divide it by 8 and then by 3 to get the answer.

## Conclusion

In conclusion, the divisibility rule for 24 is a simple and useful tool for determining if a number is divisible by 24. By checking if a number is divisible by 8 and 3, we can quickly determine if it is also divisible by 24. This rule can be particularly useful when dealing with large numbers, and can save time and effort in problem-solving situations.

## FAQs

**What is the divisibility rule for 24?**

The divisibility rule for 24 states that a number is divisible by 24 if it is divisible by both 8 and 3.

**How can the divisibility rule for 24 be used in problem-solving situations?**

The divisibility rule for 24 can be used to quickly determine if a number is divisible by 24 without having to perform long division. This can save time and effort when solving math problems.

**Can the divisibility rule for 24 be extended to other multiples of 24?**

Yes, the divisibility rule for 24 can be extended to other multiples of 24, such as 48, 72, and 96. To determine if a number is divisible by 48, for example, we would need to check if it is divisible by both 8 and 6.

**Why is it important to know divisibility rules in mathematics?**

Knowing divisibility rules can help simplify complex calculations, making it easier to solve problems and find solutions. These rules can also save time and effort, especially when dealing with large numbers.

**How can I practice using the divisibility rule for 24?**

To practice using the divisibility rule for 24, you can try applying it to different numbers and checking if they are divisible by 24. You can also try using the rule in problem-solving situations to see how it can be applied in real-life scenarios.