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

1. Identify the Number: Start with the number we want to check for divisibility by 3.
2. Sum the Digits: Add all the individual digits of the number together.
3. 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

1. 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.

1. 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.

1. 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.

1. 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.

1. 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.