# Divisibility Rule For 3 With Examples

**Divisibility Rule For 3 With Examples**

The divisibility rule for 3 is a simple method used to determine if a number is divisible by 3 without actually performing the division. The rule states that a number is divisible by 3 if the sum of its digits is divisible by 3.

### Steps to Apply the Rule

**Identify the Number:**Start with the number we want to check for divisibility by 3.**Sum the Digits:**Add all the individual digits of the number together.**Check the Sum:**Determine if the resulting sum is divisible by 3.

- If the sum is divisible by 3, then the original number is also divisible by 3.
- If the sum is not divisible by 3, then the original number is not divisible by 3.

### Examples

**Example 1: Number 123**

**Step 1:**Identify the number: 123**Step 2:**Sum the digits: (1 + 2 + 3 = 6)**Step 3:**Check the sum: 6 is divisible by 3.**Conclusion:**Therefore, 123 is divisible by 3.

**Example 2: Number 456**

**Step 1:**Identify the number: 456**Step 2:**Sum the digits: (4 + 5 + 6 = 15)**Step 3:**Check the sum: 15 is divisible by 3.**Conclusion:**Thus, 456 is divisible by 3.

**Example 3: Number 789**

**Step 1:**Identify the number: 789**Step 2:**Sum the digits: (7 + 8 + 9 = 24)**Step 3:**Check the sum: 24 is divisible by 3.**Conclusion:**Therefore, 789 is divisible by 3.

**Example 4: Number 145**

**Step 1:**Identify the number: 145**Step 2:**Sum the digits: (1 + 4 + 5 = 10)**Step 3:**Check the sum: 10 is not divisible by 3.**Conclusion:**Hence, 145 is not divisible by 3.

**Example 5: Number 99**

**Step 1:**Identify the number: 99**Step 2:**Sum the digits: (9 + 9 = 18)**Step 3:**Check the sum: 18 is divisible by 3.**Conclusion:**Thus, 99 is divisible by 3.

### Additional Points

**Negative Numbers:**The rule applies to negative numbers as well. For instance, for -123, the sum of the digits is still 1 + 2 + 3 = 6, which is divisible by 3.**Multiple Digits:**If the sum of the digits is a large number, we can apply the rule repeatedly until we get a single-digit sum.- For example, for 987654321:
- Sum the digits: (9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45)
- Check the sum: 45 is divisible by 3, so 987654321 is also divisible by 3.

### Summary

The divisibility rule for 3 is a quick and efficient way to determine if a number is divisible by 3. By simply summing the digits and checking if that sum is divisible by 3, we can easily assess divisibility without performing long division.