How Do You Know if a Digit is Divisible by 3?
A number is divisible by 3 if the sum of its digits is divisible by 3.
The divisibility rule for 3 is a simple yet powerful tool for determining whether a number is evenly divisible by 3 without performing the actual division. This rule states: A number is divisible by 3 if the sum of its digits is divisible by 3.
This rule applies to whole numbers of any size. Let's explore this with some examples:
-
Example 1: Consider the number 12. The sum of its digits is 1 + 2 = 3. Since 3 is divisible by 3, 12 is divisible by 3.
-
Example 2: Consider the number 483. The sum of its digits is 4 + 8 + 3 = 15. Since 15 is divisible by 3 (15 / 3 = 5), 483 is divisible by 3.
-
Example 3: Consider the number 71. The sum of its digits is 7 + 1 = 8. Since 8 is not divisible by 3, 71 is not divisible by 3.
Practical Application
This divisibility rule is useful in various scenarios, including:
- Mental Math: Quickly checking divisibility without a calculator.
- Error Checking: Verifying calculations, particularly in accounting or financial contexts.
- Programming: Developing efficient algorithms for divisibility checks.
Proof and Further Exploration
The divisibility rule for 3 is based on the properties of modular arithmetic and can be formally proven. A detailed mathematical proof is available in various number theory resources. For a deeper understanding, research the concepts of modular arithmetic and congruences. This rule, along with other divisibility rules (Divisibility Rules From 1 to 13 | Division Rules in Maths), provides efficient ways to check divisibility without lengthy calculations.
