Checking for Divisibility by 6

Oct 13, 2025 by recoveryshake.com 105 views

Introduction

In mathematics, divisibility is a fundamental concept that deals with the ability of a number to be divided by another number without leaving a remainder. In this article, we will explore the concept of divisibility by 6, a number that is both a multiple of 2 and 3. We will examine the given numbers and determine which ones are divisible by 6.

What is Divisibility by 6?

Divisibility by 6 is a property of a number that allows it to be divided by 6 without leaving a remainder. A number is divisible by 6 if it is both divisible by 2 and 3. This means that the number must be even (i.e., divisible by 2) and the sum of its digits must be divisible by 3.

The Given Numbers

We are given four numbers to check for divisibility by 6:

$326$
$1110$
$962364$
$154111$

Checking for Divisibility by 6

To check if a number is divisible by 6, we need to check if it is divisible by both 2 and 3. We can use the following steps:

Check if the number is even (i.e., divisible by 2). If it is not even, it is not divisible by 6.
Check if the sum of the digits of the number is divisible by 3. If it is not, the number is not divisible by 6.

Checking the First Number: 326

Let's start by checking the first number, 326.

Is 326 even? Yes, it is even, so we can proceed to the next step.
What is the sum of the digits of 326? The sum of the digits is 3 + 2 + 6 = 11.
Is 11 divisible by 3? No, it is not, so 326 is not divisible by 6.

Checking the Second Number: 1110

Now, let's check the second number, 1110.

Is 1110 even? Yes, it is even, so we can proceed to the next step.
What is the sum of the digits of 1110? The sum of the digits is 1 + 1 + 1 + 0 = 3.
Is 3 divisible by 3? Yes, it is, so 1110 is divisible by 6.

Checking the Third Number: 962364

Next, let's check the third number, 962364.

Is 962364 even? Yes, it is even, so we can proceed to the next step.
What is the sum of the digits of 962364? The sum of the digits is 9 + 6 + 2 + 3 + 6 + 4 = 30.
Is 30 divisible by 3? Yes, it is, so 962364 is divisible by 6.

Checking the Fourth Number: 154111

Finally, let's check the fourth number, 154111.

Is 154111 even? No, it is not even, so it is not divisible by 6.

Conclusion

In conclusion, we have checked the given numbers for divisibility by 6 and found that:

$326$$ is not divisible by 6.$
$1110$$ is divisible by 6.$
$962364$$ is divisible by 6.$
$154111$$ is not divisible by 6.$

Divisibility by 6: A Summary

In this article, we have explored the concept of divisibility by 6 and applied it to the given numbers. We have seen that a number is divisible by 6 if it is both divisible by 2 and 3. We have also seen that the sum of the digits of a number must be divisible by 3 for the number to be divisible by 6. We hope that this article has provided a clear understanding of the concept of divisibility by 6 and how to apply it to check if a number is divisible by 6.

Frequently Asked Questions

Q: What is divisibility by 6?

A: Divisibility by 6 is a property of a number that allows it to be divided by 6 without leaving a remainder. A number is divisible by 6 if it is both divisible by 2 and 3.

Q: How do I check if a number is divisible by 6?

A: To check if a number is divisible by 6, you need to check if it is divisible by both 2 and 3. You can use the following steps:

Check if the number is even (i.e., divisible by 2). If it is not even, it is not divisible by 6.
Check if the sum of the digits of the number is divisible by 3. If it is not, the number is not divisible by 6.

Q: What is the sum of the digits of a number?

A: The sum of the digits of a number is the sum of the individual digits of the number. For example, the sum of the digits of 123 is 1 + 2 + 3 = 6.

Q: Is 6 divisible by 6?

A: Yes, 6 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 12 divisible by 6?

A: Yes, 12 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 15 divisible by 6?

A: No, 15 is not divisible by 6 because it is not divisible by 2.

Q: Is 18 divisible by 6?

A: Yes, 18 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 24 divisible by 6?

A: Yes, 24 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 30 divisible by 6?

A: Yes, 30 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 36 divisible by 6?

A: Yes, 36 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 42 divisible by 6?

A: Yes, 42 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 48 divisible by 6?

A: Yes, 48 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 54 divisible by 6?

A: Yes, 54 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 60 divisible by 6?

A: Yes, 60 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 66 divisible by 6?

A: Yes, 66 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 72 divisible by 6?

A: Yes, 72 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 78 divisible by 6?

A: Yes, 78 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 84 divisible by 6?

A: Yes, 84 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 90 divisible by 6?

A: Yes, 90 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 96 divisible by 6?

A: Yes, 96 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 102 divisible by 6?

A: Yes, 102 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 108 divisible by 6?

A: Yes, 108 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 114 divisible by 6?

A: Yes, 114 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 120 divisible by 6?

A: Yes, 120 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 126 divisible by 6?

A: Yes, 126 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 132 divisible by 6?

A: Yes, 132 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 138 divisible by 6?

A: Yes, 138 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 144 divisible by 6?

A: Yes, 144 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 150 divisible by 6?

A: Yes, 150 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 156 divisible by 6?

Q: What is divisibility by 6?

A: Divisibility by 6 is a property of a number that allows it to be divided by 6 without leaving a remainder. A number is divisible by 6 if it is both divisible by 2 and 3.

Q: How do I check if a number is divisible by 6?

A: To check if a number is divisible by 6, you need to check if it is divisible by both 2 and 3. You can use the following steps:

Check if the number is even (i.e., divisible by 2). If it is not even, it is not divisible by 6.
Check if the sum of the digits of the number is divisible by 3. If it is not, the number is not divisible by 6.

Q: What is the sum of the digits of a number?

A: The sum of the digits of a number is the sum of the individual digits of the number. For example, the sum of the digits of 123 is 1 + 2 + 3 = 6.

Q: Is 6 divisible by 6?

A: Yes, 6 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 12 divisible by 6?

A: Yes, 12 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 15 divisible by 6?

A: No, 15 is not divisible by 6 because it is not divisible by 2.

Q: Is 18 divisible by 6?

A: Yes, 18 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 24 divisible by 6?

A: Yes, 24 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 30 divisible by 6?

A: Yes, 30 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 36 divisible by 6?

A: Yes, 36 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 42 divisible by 6?

A: Yes, 42 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 48 divisible by 6?

A: Yes, 48 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 54 divisible by 6?

A: Yes, 54 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 60 divisible by 6?

A: Yes, 60 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 66 divisible by 6?

A: Yes, 66 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 72 divisible by 6?

A: Yes, 72 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 78 divisible by 6?

A: Yes, 78 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 84 divisible by 6?

A: Yes, 84 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 90 divisible by 6?

A: Yes, 90 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 96 divisible by 6?

A: Yes, 96 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 102 divisible by 6?

A: Yes, 102 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 108 divisible by 6?

A: Yes, 108 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 114 divisible by 6?

A: Yes, 114 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 120 divisible by 6?

A: Yes, 120 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 126 divisible by 6?

A: Yes, 126 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 132 divisible by 6?

A: Yes, 132 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 138 divisible by 6?

A: Yes, 138 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 144 divisible by 6?

A: Yes, 144 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 150 divisible by 6?

A: Yes, 150 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 156 divisible by 6?

A: Yes, 156 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 162 divisible by 6?

A: Yes, 162 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 168 divisible by 6?

A: Yes, 168 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 174 divisible by 6?

A: Yes, 174 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 180 divisible by 6?

A: Yes, 180 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 186 divisible by 6?

A: Yes, 186 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 192 divisible by 6?

A: Yes, 192 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 198 divisible by 6?

A: Yes, 198 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 204 divisible by 6?

A: Yes, 204 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 210 divisible by 6?

A: Yes, 210 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 216 divisible by 6?

A: Yes, 216 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 222 divisible by 6?

A: Yes, 222 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 228 divisible by 6?

A: Yes, 228 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 234 divisible by 6?

A: Yes, 234 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 240 divisible by 6?

A: Yes, 240 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 246 divisible by 6?

A: Yes, 246 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 252 divisible by 6?

A: Yes, 252 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 258 divisible by 6?

A: Yes, 258 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 264 divisible by 6?

A: Yes, 264 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 270 divisible by 6?

A: Yes, 270 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 276 divisible by 6?

A: Yes, 276 is divisible by 6 because it is both divisible by 2 and 3.

Q: Is 282 divisible by 6?

A: Yes, 282 is divisible by 6 because it is both divisible by 2 and 3.