Divisibility Rule For 15 With Examples

Divisibility Rule for 15

The divisibility rule for 15 is straightforward and involves checking divisibility by both 3 and 5, since 15 is the product of these two numbers.

A number is divisible by 15 if it meets the criteria for both 3 and 5.

Here’s how to determine if a number is divisible by 15:

This means we need to check two conditions:

1. Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
2. Divisibility by 5: A number is divisible by 5 if its last digit is either 0 or 5.

Steps to Check Divisibility by 15

1. Check Divisibility by 3:

• Add the digits of the number together.
• If the sum is divisible by 3, then the number meets this condition.

1. Check Divisibility by 5:

• Look at the last digit of the number.
• If it is 0 or 5, then the number meets this condition.

1. Conclusion:

• If both conditions are satisfied, then the original number is divisible by 15.

Example Walkthroughs

Example 1: 105

1. Check Divisibility by 3:

• Digits: 1, 0, 5
• Sum: (1 + 0 + 5 = 6)
• (6/3 = 2) (with no remainder).
• Conclusion: 105 is divisible by 3.

1. Check Divisibility by 5:

• Last digit: 5
• Conclusion: 105 is divisible by 5.

1. Final Conclusion: Since 105 is divisible by both 3 and 5, 105 is divisible by 15.

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Example 2: 150

1. Check Divisibility by 3:

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

1. Check Divisibility by 5:

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

1. Final Conclusion: Since 150 is divisible by both 3 and 5, 150 is divisible by 15.

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Example 3: 56

1. Check Divisibility by 3:

• Digits: 5, 6
• Sum: (5 + 6 = 11)
• (11/3 ≈ 3.67) (not an integer, remainder exists).
• Conclusion: 56 is not divisible by 3.

1. Check Divisibility by 5:

• Last digit: 6
• Conclusion: 56 is not divisible by 5.

1. Final Conclusion: Since 56 is not divisible by 3 or 5, it is not divisible by 15.

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Example 4: 225

1. Check Divisibility by 3:

• Digits: 2, 2, 5
• Sum: (2 + 2 + 5 = 9)
• (9/3 = 3) (with no remainder).
• Conclusion: 225 is divisible by 3.

1. Check Divisibility by 5:

• Last digit: 5
• Conclusion: 225 is divisible by 5.

1. Final Conclusion: Since 225 is divisible by both 3 and 5, 225 is divisible by 15.

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Example 5: 58

1. Check Divisibility by 3:

• Digits: 5, 8
• Sum: (5 + 8 = 13)
• (13/3 ≈ 4.33) (not an integer, remainder exists).
• Conclusion: 58 is not divisible by 3.

1. Check Divisibility by 5:

• Last digit: 8
• Conclusion: 58 is not divisible by 5.

1. Final Conclusion: Since 58 is not divisible by 3 or 5, it is not divisible by 15.

Divisibility Rule for 15

A number is divisible by 15 if:

1. It is divisible by 5 (the last digit is 0 or 5).
2. It is divisible by 3 (the sum of the digits is divisible by 3).

Steps to Check Divisibility by 15

1. Check if the number is divisible by 5:

• Look at the last digit. If it’s 0 or 5, the number is divisible by 5.

1. Check if the number is divisible by 3:

• Add the digits of the number together. If the sum is divisible by 3, then the number is divisible by 3.

Example 1: Check if 75 is Divisible by 15

1. Check divisibility by 5:

• Last digit is 5 (divisible by 5).

1. Check divisibility by 3:

• Sum of the digits: (7 + 5 = 12) (12 is divisible by 3).

1. Conclusion: Since 75 is divisible by both 5 and 3, it is divisible by 15.

Example 2: Check if 120 is Divisible by 15

1. Check divisibility by 5:

• Last digit is 0 (divisible by 5).

1. Check divisibility by 3:

• Sum of the digits: (1 + 2 + 0 = 3) (3 is divisible by 3).

1. Conclusion: Since 120 is divisible by both 5 and 3, it is divisible by 15.

Example 3: Check if 44 is Divisible by 15

1. Check divisibility by 5:

• Last digit is 4 (not divisible by 5).

1. Conclusion: Since 44 is not divisible by 5, it cannot be divisible by 15.

Example 4: Check if 90 is Divisible by 15

1. Check divisibility by 5:

• Last digit is 0 (divisible by 5).

1. Check divisibility by 3:

• Sum of the digits: (9 + 0 = 9) (9 is divisible by 3).

1. Conclusion: Since 90 is divisible by both 5 and 3, it is divisible by 15.

Example 5: Check if 32 is Divisible by 15

1. Check divisibility by 5:

• Last digit is 2 (not divisible by 5).

1. Conclusion: Since 32 is not divisible by 5, it cannot be divisible by 15.

Summary

To check if a number is divisible by 15:

1. Confirm it is divisible by 5 (last digit is 0 or 5).
2. Confirm it is divisible by 3 (sum of the digits is divisible by 3).

If both conditions are met, the number is divisible by 15.

This rule is efficient for quickly assessing divisibility without performing lengthy calculations.