The Least 3-Digit Number Divisible by 6: Answering the Question and Exploring Further

When dealing with divisibility questions, it is essential to have a clear understanding of the properties and characteristics of numbers. This article aims to provide insightful information regarding the least 3-digit number that is divisible by 6. We will explore the solution, delve into the underlying mathematics, and provide additional context to help clarify any doubts.

Understanding the Question

The question asks for the least 3-digit number that is divisible by 6. This is a straightforward problem in number theory. To address this, we need to identify the smallest 3-digit number that is both even and divisible by 3 (since a number is divisible by 6 if and only if it is divisible by both 2 and 3).

Initial Analysis

The smallest 3-digit number is 100. However, 100 is not divisible by 6 since it is not evenly divisible by both 2 and 3. Specifically, 100 is divisible by 2 but not by 3. The next number, 101, is also not divisible by 6. However, the number 102 is divisible by 6 because:

102 div; 6 17, and ( 17 times 6 102 ). Therefore, the smallest 3-digit number that is divisible by 6 is 102.

Including Negative Numbers

It is important to note that there is another perspective to this question, which is to include negative numbers. In this case, we would need to find the lowest 3-digit integer that is divisible by 6. The smallest 3-digit integer is -999. The number -999 is not divisible by 6, but -996 is divisible by 6:

-996 div; 6 -166, and ( -166 times 6 -996 ). Therefore, the lowest 3-digit integer that is divisible by 6 is -996.

Further Exploration

Numbers that are divisible by 6 have interesting properties. For example, they are always even and can be expressed as a product of 2 and another integer that is divisible by 3. Additionally, these numbers can be found by checking whether the number is divisible by both 2 and 3.

The First Three-Digit Numbers Divisible by 6

The first three-digit number that is divisible by 6 is 102. Following 102, the next numbers that are divisible by 6 are 108, 114, 120, and so on. These numbers form an arithmetic sequence with a common difference of 6.

Conclusion

In summary, the least 3-digit number divisible by 6 is 102. However, if negative numbers are included, the lowest 3-digit integer divisible by 6 is -996. Understanding and solving such problems enhances number sense and provides insights into the properties of divisibility.

For further reading and practice, you may want to explore more about number theory, divisibility rules, and arithmetic sequences. These concepts are fundamental in mathematics and have numerous applications in various fields, including computer science and cryptography.

Whether you are preparing for math competitions, enhancing your mathematical skills, or simply curious about the properties of numbers, this knowledge will undoubtedly be valuable.