Divisibility Rule For 30 With Examples

Divisibility Rule For 30

The divisibility rule for 30 is based on its prime factors: (2), (3), and (5). A number is divisible by 30 if it is divisible by all three of these factors. Here’s a detailed breakdown of the rule and how to apply it.

Divisibility Rules for 30

1. Divisibility by 2: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).
2. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
3. Divisibility by 5: A number is divisible by 5 if its last digit is either 0 or 5.

The divisibility rule for 30 is based on its prime factors: (2), (3), and (5). A number is divisible by 30 if it satisfies the conditions for all three factors. Here’s a detailed explanation of how to check for divisibility by 30, along with examples.

Divisibility Rules for 30

1. Divisibility by 2:

• A number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8).

1. Divisibility by 3:

• A number is divisible by 3 if the sum of its digits is divisible by 3.

1. Divisibility by 5:

• A number is divisible by 5 if its last digit is either 0 or 5.

Combined Rule

For a number to be divisible by 30, it must meet all three conditions:

• It must be even (divisible by 2).
• The sum of its digits must be divisible by 3.
• Its last digit must be either 0 or 5 (divisible by 5).

Examples

Example 1: Check if 120 is divisible by 30

1. Check for 2:

• Last digit: 0 (even).
• Conclusion: 120 is divisible by 2.

1. Check for 3:

• Sum of digits: (1 + 2 + 0 = 3).
• (3/3 = 1) (no remainder).
• Conclusion: 120 is divisible by 3.

1. Check for 5:

• Last digit: 0.
• Conclusion: 120 is divisible by 5.

Since 120 is divisible by 2, 3, and 5, it is divisible by 30.

Example 2: Check if 45 is divisible by 30

1. Check for 2:

• Last digit: 5 (odd).
• Conclusion: 45 is not divisible by 2.

Since 45 is not divisible by 2, it is not divisible by 30.

Example 3: Check if 150 is divisible by 30

1. Check for 2:

• Last digit: 0 (even).
• Conclusion: 150 is divisible by 2.

1. Check for 3:

• Sum of digits: (1 + 5 + 0 = 6).
• (6/3 = 2) (no remainder).
• Conclusion: 150 is divisible by 3.

1. Check for 5:

• Last digit: 0.
• Conclusion: 150 is divisible by 5.

Since 150 is divisible by 2, 3, and 5, it is divisible by 30.

Example 4: Check if 234 is divisible by 30

1. Check for 2:

• Last digit: 4 (even).
• Conclusion: 234 is divisible by 2.

1. Check for 3:

• Sum of digits: (2 + 3 + 4 = 9).
• (9/3 = 3) (no remainder).
• Conclusion: 234 is divisible by 3.

1. Check for 5:

• Last digit: 4.
• Conclusion: 234 is not divisible by 5.

Since 234 is not divisible by 5, it is not divisible by 30.

Example 5: Check if 600 is divisible by 30

1. Check for 2:

• Last digit: 0 (even).
• Conclusion: 600 is divisible by 2.

1. Check for 3:

• Sum of digits: (6 + 0 + 0 = 6).
• (6/3 = 2) (no remainder).
• Conclusion: 600 is divisible by 3.

1. Check for 5:

• Last digit: 0.
• Conclusion: 600 is divisible by 5.

Since 600 is divisible by 2, 3, and 5, it is divisible by 30.

Summary

To determine if a number is divisible by 30:

1. Check if it is even (last digit is 0, 2, 4, 6, or 8).
2. Check if the sum of its digits is divisible by 3.
3. Check if its last digit is either 0 or 5.

If a number meets all three criteria, it is divisible by 30. This method provides a clear and efficient way to assess divisibility.