Which of the following numbers is divisible by 3? This question often arises in various mathematical contexts, whether it’s a simple arithmetic problem or a more complex algebraic equation. Understanding divisibility by 3 is essential for mastering fundamental mathematical concepts and solving problems efficiently. In this article, we will explore the characteristics of numbers divisible by 3 and provide some examples to illustrate the concept.
Divisibility by 3 is a fundamental concept in number theory, which deals with the properties of integers. A number is divisible by 3 if it can be evenly divided by 3 without leaving a remainder. To determine if a number is divisible by 3, you can use the following methods:
1. Sum of digits: Add the digits of the number together. If the sum is divisible by 3, then the original number is also divisible by 3. For example, consider the number 123. The sum of its digits is 1 + 2 + 3 = 6, which is divisible by 3. Therefore, 123 is divisible by 3.
2. Divisibility rule: A number is divisible by 3 if the difference between the sum of its digits at odd positions and the sum of its digits at even positions is divisible by 3. For instance, consider the number 456. The sum of its digits at odd positions is 4 + 6 = 10, and the sum of its digits at even positions is 5. The difference between these sums is 10 – 5 = 5, which is not divisible by 3. Hence, 456 is not divisible by 3.
Let’s look at some examples to better understand the concept:
1. 12 is divisible by 3 because the sum of its digits is 1 + 2 = 3, which is divisible by 3.
2. 18 is divisible by 3 because the difference between the sum of its digits at odd positions (1 + 8 = 9) and the sum of its digits at even positions (0) is 9, which is divisible by 3.
3. 27 is divisible by 3 because the sum of its digits is 2 + 7 = 9, which is divisible by 3.
In conclusion, understanding which of the following numbers is divisible by 3 is crucial for solving various mathematical problems. By applying the sum of digits method or the divisibility rule, you can quickly determine if a number is divisible by 3. This knowledge will help you develop a strong foundation in number theory and enhance your mathematical skills.
