Divisibility Rule For 28 With Examples

Divisibility Rule For 28

The divisibility rule for 28 is based on its prime factors, specifically (4) and (7), since (28 = 4 x 7). For a number to be divisible by 28, it must satisfy the divisibility rules for both (4) and (7).

Divisibility Rules for 28

1. Divisibility by 4: A number is divisible by 4 if the last two digits of the number form a number that is divisible by 4.
2. Divisibility by 7: To check if a number is divisible by 7, we can use the following method:

• Double the last digit and subtract it from the rest of the number. If the result is divisible by 7 (including if it’s 0), then the original number is divisible by 7.

Combined Rule

For a number to be divisible by 28, it must be divisible by both (4) and (7).

Examples

Example 1: Check if 112 is divisible by 28

1. Check for 4:

• Last two digits: 12
• (12/4 = 3) (no remainder).
• Conclusion: 112 is divisible by 4.

1. Check for 7:

• Last digit: 2, rest of the number: 11
• Double the last digit: (2 x 2 = 4)
• Subtract: (11 – 4 = 7)
• (7/7 = 1) (no remainder).
• Conclusion: 112 is divisible by 7.

Since 112 is divisible by both 4 and 7, it is divisible by 28.

Example 2: Check if 156 is divisible by 28

1. Check for 4:

• Last two digits: 56
• (56/4 = 14) (no remainder).
• Conclusion: 156 is divisible by 4.

1. Check for 7:

• Last digit: 6, rest of the number: 15
• Double the last digit: (6 x 2 = 12)
• Subtract: (15 – 12 = 3)
• (3/7) (not divisible).
• Conclusion: 156 is not divisible by 7.

Since 156 is not divisible by 7, it is not divisible by 28.

Example 3: Check if 224 is divisible by 28

1. Check for 4:

• Last two digits: 24
• (24/4 = 6) (no remainder).
• Conclusion: 224 is divisible by 4.

1. Check for 7:

• Last digit: 4, rest of the number: 22
• Double the last digit: (4 x 2 = 8)
• Subtract: (22 – 8 = 14)
• (14/7 = 2) (no remainder).
• Conclusion: 224 is divisible by 7.

Since 224 is divisible by both 4 and 7, it is divisible by 28.

Example 4: Check if 100 is divisible by 28

1. Check for 4:

• Last two digits: 00
• (0/4 = 0) (no remainder).
• Conclusion: 100 is divisible by 4.

1. Check for 7:

• Last digit: 0, rest of the number: 10
• Double the last digit: (0 x 2 = 0)
• Subtract: (10 – 0 = 10)
• (10/7) (not divisible).
• Conclusion: 100 is not divisible by 7.

Since 100 is not divisible by 7, it is not divisible by 28.

Example 5: Check if 336 is divisible by 28

1. Check for 4:

• Last two digits: 36
• (36/4 = 9) (no remainder).
• Conclusion: 336 is divisible by 4.

1. Check for 7:

• Last digit: 6, rest of the number: 33
• Double the last digit: (6 x 2 = 12)
• Subtract: (33 – 12 = 21)
• (21/7 = 3) (no remainder).
• Conclusion: 336 is divisible by 7.

Since 336 is divisible by both 4 and 7, it is divisible by 28.

Summary

To determine if a number is divisible by 28:

1. Check if it is divisible by 4 (last two digits).
2. Check if it is divisible by 7 (using the doubling and subtracting method).

If both conditions are satisfied, the number is divisible by 28. This method allows for quick assessments using basic arithmetic.