Divisibility rules are a set of tricks that help us determine whether a number is divisible by another number without actually dividing them. One of the most important and useful rules is the divisibility rule for 6. In this article, we will explore this rule in detail and learn how to use it effectively. So, let’s dive in!

## What is the divisibility rule for 6?

The divisibility rule for 6 states that a number is divisible by 6 if it is divisible by both 2 and 3. In other words, if a number is even and the sum of its digits is divisible by 3, then it is divisible by 6.

## How does the divisibility rule for 6 work?

The divisibility rule for 6 works by taking advantage of the fact that 6 is the product of 2 and 3. Since any even number is divisible by 2, we only need to check if the number is divisible by 3. To do this, we add up the digits of the number and check if the sum is divisible by 3. If it is, then the number is divisible by 3 and hence by 6 as well.

## Examples of the divisibility rule for 6

### Example 1:

Let’s take the number 576. We know that it is even because it ends in 6, which is an even digit. Now, let’s add up its digits:

**5 + 7 + 6 = 18**

Since 18 is divisible by 3, we can conclude that 576 is divisible by 6.

### Example 2:

Now, let’s take the number 2436. We know that it is even because it ends in 6, which is an even digit. Now, let’s add up its digits:

**2 + 4 + 3 + 6 = 15**

Since 15 is divisible by 3, we can conclude that 2436 is divisible by 6.

## Why is the divisibility rule for 6 important?

The divisibility rule for 6 is important because it can save a lot of time and effort when dealing with large numbers. Instead of performing long division or using a calculator, we can simply apply the rule to determine whether a number is divisible by 6 or not. This can be particularly useful in math competitions or exams where time is limited.

## Tips for using the divisibility rule for 6 effectively

Here are some tips for using the divisibility rule for 6 effectively:

- Always check if the number is even first, as this is a necessary condition for it to be divisible by 6.
- Break up the number into smaller parts to make it easier to add up the digits.
- If the sum of the digits is not immediately divisible by 3, try subtracting or adding multiples of 3 to the sum until it is.

## Other divisibility rules to know

In addition to the divisibility rule for 6, there are several other rules that can be useful in determining whether a number is divisible by another number. Some of these include:

- Divisibility rule for 2
- Divisibility rule for 3
- Divisibility rule for 4
- Divisibility rule for 5
- Divisibility rule for 9
- Divisibility rule for 10

It’s always helpful to have these rules in your arsenal when working with numbers. They can make calculations easier and save you a lot of time.

## FAQs

### What is the difference between the divisibility rule for 6 and the rule for 3?

The divisibility rule for 6 requires a number to be even and have a digit sum that is divisible by 3, while the rule for 3 only requires the digit sum to be divisible by 3. In other words, the rule for 6 is more specific and hence more restrictive.

### Can the divisibility rule for 6 be applied to decimal numbers?

No, the divisibility rule for 6 only applies to whole numbers or integers. It cannot be applied to decimal numbers or fractions.

### What is the divisibility rule for 7?

The divisibility rule for 7 states that a number is divisible by 7 if and only if the difference between twice the unit digit and the remaining digits is divisible by 7.

### Can the divisibility rule for 6 be used for larger numbers?

Yes, the divisibility rule for 6 can be used for larger numbers as well. The process is the same – check if the number is even and if the sum of its digits is divisible by 3.

### Are divisibility rules only used in math competitions or exams?

No, divisibility rules are useful in everyday life as well. They can help you quickly determine if a number is divisible by another number, which can be useful in many situations such as calculating discounts or dividing tasks among a group of people.

## Conclusion

In conclusion, the divisibility rule for 6 is a useful trick that can help us determine whether a number is divisible by 6 quickly and easily. By checking if a number is even and if the sum of its digits is divisible by 3, we can determine if it’s divisible by 6 as well. Remember to use this rule in combination with other divisibility rules for best results, and practice with different numbers to become proficient.