The set of integers divisible by 3 consists of all numbers that can be divided by 3 with no remainder. This set includes both positive and negative numbers.
Examples of integers divisible by 3:
- Positive numbers: 3, 6, 9, 12, 15, 18, 21...
- Negative numbers: -3, -6, -9, -12, -15, -18, -21...
Understanding the Concept:
Numbers divisible by 3 are multiples of 3. This means they can be expressed as 3 multiplied by an integer.
- For example, 12 is divisible by 3 because 12 = 3 x 4.
Practical Insights:
- Divisibility rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3. For example, the number 123 is divisible by 3 because 1 + 2 + 3 = 6, which is divisible by 3.
In conclusion, the set of integers divisible by 3 is an infinite set containing all numbers that can be divided by 3 without leaving a remainder.
