The divisibility rule of 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3.
Example:
- The number 123 is divisible by 3 because the sum of its digits (1 + 2 + 3 = 6) is divisible by 3.
Explanation:
This rule works because of the way our number system is based on powers of 10.
- Any power of 10 can be expressed as 1 more than a multiple of 3 (e.g., 10 = 9 + 1, 100 = 99 + 1, 1000 = 999 + 1).
- Therefore, when you expand a number in terms of its digits, you're essentially adding a multiple of 3 (from the powers of 10) and the sum of the digits.
- For the whole number to be divisible by 3, the sum of the digits must also be divisible by 3.
Practical Insights:
This rule can be used to quickly check whether a number is divisible by 3 without performing the actual division. This is especially helpful when dealing with large numbers.
