When it comes to divisibility rules, most people are familiar with the rules for 2, 3, 5, 6, 9, and 10. However, there are many other divisibility rules that can make math problems easier to solve. One such rule is the divisibility rule for 14. In this article, we will discuss what the rule is, how to apply it, and why it is important.

## What is the divisibility rule for 14?

The divisibility rule for 14 states that a number is divisible by 14 if and only if it is divisible by both 2 and 7. In other words, if a number is even and has a digit sum that is divisible by 7, then it is divisible by 14.

## How to apply the divisibility rule for 14

To apply the divisibility rule for 14, you first need to check if the number is even. If it is not even, then it is not divisible by 14. If it is even, then you need to find the digit sum of the number. The digit sum is the sum of all the digits in the number. For example, the digit sum of 182 is 1+8+2=11.

Once you have the digit sum, you need to check if it is divisible by 7. If it is, then the number is divisible by 14. If it is not, then the number is not divisible by 14.

## Examples of the divisibility rule for 14 in action

Let’s take the number 112 as an example. Is it divisible by 14?

First, we check if it is even. Since the last digit is even, we know that it is.

Next, we find the digit sum. The digit sum of 112 is 1+1+2=4.

Since 4 is not divisible by 7, we know that 112 is not divisible by 14.

Now let’s take the number 168. Is it divisible by 14?

First, we check if it is even. Since the last digit is even, we know that it is.

Next, we find the digit sum. The digit sum of 168 is 1+6+8=15.

Since 15 is divisible by 7, we know that 168 is divisible by 14.

## Why is the divisibility rule for 14 important?

The divisibility rule for 14 is important because it can make math problems easier to solve. If you are trying to find all the factors of a large number, for example, you can use the divisibility rule for 14 to quickly eliminate numbers that are not factors. This can save you time and effort.

## Divisibility rule for 14 vs. other rules

Compared to some of the other divisibility rules, such as the rules for 2, 3, 5, and 10, the rule for 14 is not as well-known. However, it is still a useful rule to know, especially when dealing with larger numbers or when you need to quickly eliminate numbers that are not factors. Additionally, unlike some of the other rules, the rule for 14 checks for divisibility by both 2 and 7, which can help catch errors in your calculations.

## Divisibility rule for 14 in real-world applications

The divisibility rule for 14 can also be useful in real-world applications. For example, if you are trying to divide a certain number of items among a group of people, you can use the rule for 14 to determine how many groups you need to create to ensure each person gets an equal number of items. This can be helpful in situations such as distributing party favors, organizing group activities, or dividing up a potluck meal.

## Common mistakes to avoid when using the rule

One common mistake to avoid when using the rule for 14 is forgetting to check if the number is even before finding the digit sum. If the number is odd, it cannot be divisible by 14, and you do not need to check the digit sum.

Another mistake to avoid is miscomputing the digit sum. Make sure to add up all the digits in the number correctly and double-check your math before using the rule.

## Tips for mastering the divisibility rule for 14

To master the divisibility rule for 14, it is important to practice using the rule with different numbers. You can also try combining the rule for 14 with other rules, such as the rule for 2 or the rule for 7, to quickly determine if a number is divisible by multiple factors.

Additionally, it can be helpful to memorize the multiples of 14 up to a certain number, such as 100 or 1000, to quickly recognize which numbers are divisible by 14.

## 10. FAQs

### What is a digit sum?

A digit sum is the sum of all the digits in a number.

### Is the divisibility rule for 14 commonly used?

While the rule for 14 is not as well-known as some of the other divisibility rules, it can still be useful in certain situations.

### Can the rule for 14 be used to determine if a number is divisible by 2 or 7?

Yes, the rule for 14 checks for divisibility by both 2 and 7.

### Are there any tricks to quickly find the digit sum of a number?

One trick is to add the first and last digits of the number, then add the second and second-to-last digits, and so on, until you reach the middle of the number.

### How can the rule for 14 be useful in real-world situations?

The rule for 14 can be used to evenly distribute items among a group of people or to quickly eliminate non-factors when trying to find all the factors of a large number.

## Conclusion

In conclusion, the divisibility rule for 14 can be a valuable tool for solving math problems and real-world applications. By checking if a number is even and has a digit sum that is divisible by 7, you can quickly determine if a number is divisible by 14. Remember to avoid common mistakes and practice using the rule with different numbers to master it.