How to Tell If a Number Is Divisible by 6
Divisibility is a fundamental concept in mathematics that helps us understand the relationships between numbers. One of the most common divisibility rules is to determine if a number is divisible by 6. Knowing how to tell if a number is divisible by 6 can be particularly useful in various real-life situations, such as solving math problems, simplifying fractions, or even in everyday tasks like counting items in groups. In this article, we will explore the steps and methods to determine if a number is divisible by 6.
Firstly, it is essential to understand that a number is divisible by 6 if it is divisible by both 2 and 3. This is because 6 is the product of 2 and 3 (6 = 2 × 3). Therefore, to check if a number is divisible by 6, you need to verify its divisibility by both 2 and 3.
To check for divisibility by 2, you can follow these steps:
1. Look at the last digit of the number.
2. If the last digit is even (0, 2, 4, 6, or 8), then the number is divisible by 2.
3. If the last digit is odd (1, 3, 5, 7, or 9), then the number is not divisible by 2.
Once you have determined that the number is divisible by 2, you can move on to checking its divisibility by 3. Here’s how to do it:
1. Add up all the digits of the number.
2. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.
3. If the sum of the digits is not divisible by 3, then the original number is not divisible by 3.
By combining these two checks, you can determine if a number is divisible by 6. Here’s an example:
Let’s say you want to check if the number 42 is divisible by 6.
1. Check divisibility by 2: The last digit of 42 is 2, which is even. Therefore, 42 is divisible by 2.
2. Check divisibility by 3: Add up the digits of 42: 4 + 2 = 6. Since 6 is divisible by 3, 42 is also divisible by 3.
Since 42 is divisible by both 2 and 3, we can conclude that it is divisible by 6.
In conclusion, to tell if a number is divisible by 6, you need to check its divisibility by both 2 and 3. By following the steps outlined in this article, you can easily determine if a number is divisible by 6 and apply this knowledge in various mathematical and real-life scenarios.
