If you have ever struggled with long division or multiplication problems, you may have wondered if there is an easier way to determine if a number is divisible by another number. Thankfully, there are a number of divisibility rules that can make these calculations easier and more efficient. In this article, we will explore the divisibility rule for 21 and its application in solving math problems.

## Divisibility Rule for 21

The divisibility rule for 21 is a method for determining if a number is divisible by 21 without having to perform long division. To use this rule, we must first understand that 21 is equal to 3 times 7. This means that if a number is divisible by both 3 and 7, it is also divisible by 21.

**To apply this rule, we can follow these steps:**

- Determine if the number is divisible by 3. We can do this by adding up the digits of the number and checking if the sum is divisible by 3. For example, the number 315 is divisible by 3 because 3 + 1 + 5 = 9, which is divisible by 3.
- Determine if the number is divisible by 7. There are a few different methods for determining if a number is divisible by 7, but one common method is to double the units digit of the number and subtract that from the remaining digits. If the resulting number is divisible by 7, then the original number is also divisible by 7. For example, the number 812 is divisible by 7 because 81 – 2(2) = 77, which is divisible by 7.
- If the number is divisible by both 3 and 7, it is also divisible by 21.

## Examples of Using the Divisibility Rule for 21

Let’s look at a few examples of how to use the divisibility rule for 21 in practice.

### Example 1

Is the number 294 divisible by 21?

- We can determine if the number is divisible by 3 by adding up its digits: 2 + 9 + 4 = 15. Since 15 is divisible by 3, we can move on to step 2.
- We can determine if the number is divisible by 7 by using the doubling and subtraction method: 29 – 2(4) = 21. Since 21 is divisible by 7, we know that the original number is also divisible by 7.
- Since the number is divisible by both 3 and 7, it is also divisible by 21.

Therefore, 294 is divisible by 21.

### Example 2

Is the number 857 divisible by 21?

- We can determine if the number is divisible by 3 by adding up its digits: 8 + 5 + 7 = 20. Since 20 is not divisible by 3, we know that the number is not divisible by 21.

Therefore, 857 is not divisible by 21.

## Why Use the Divisibility Rule for 21?

You may be wondering why it is useful to know the divisibility rule for 21.

After all, long division and multiplication are not particularly difficult once you understand the process. However, there are a few reasons why the divisibility rule for 21 can be useful:

- Speed: Using the divisibility rule can be much faster than performing long division, especially for larger numbers.
- Mental math: The rule requires some mental math skills, which can be a helpful exercise for keeping your mind sharp.
- Problem solving: Understanding divisibility rules can help you solve more complex math problems, as it allows you to break down larger numbers into their factors more easily.

## Other Divisibility Rules

The divisibility rule for 21 is just one of many divisibility rules that can be useful in math. Here are a few other commonly used rules:

- Divisibility by 2: A number is divisible by 2 if its units digit is even (i.e. 0, 2, 4, 6, or 8).
- Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
- Divisibility by 4: A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- Divisibility by 5: A number is divisible by 5 if its units digit is 0 or 5.
- Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3.
- Divisibility by 8: A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
- Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
- Divisibility by 10: A number is divisible by 10 if its units digit is 0.

## Conclusion

The divisibility rule for 21 can be a useful tool for quickly determining if a number is divisible by 21. By understanding the factors of 21 and applying the rule correctly, you can save time and mental effort when solving math problems. However, it is important to note that divisibility rules are just one method for solving math problems, and should be used in conjunction with other problem-solving strategies.

## FAQs

**Can the divisibility rule for 21 be used for numbers larger than three digits?**

Yes, the rule can be used for numbers of any size.

**Is the divisibility rule for 21 the only way to determine if a number is divisible by 21?**

No, long division can also be used to determine divisibility by 21.

**Are there other rules for determining if a number is divisible by two factors?**

Yes, there are rules for determining divisibility by many different factors.

**Can the divisibility rule for 21 be used for other multiples of 3 and 7?**

Yes, the rule can be adapted for multiples of 3 and 7, such as 42 or 63.

**Are there any exceptions to the divisibility rule for 21?**

No, if a number is divisible by both 3 and 7, it is always divisible by 21.