Divisibility Rule For 22 With Examples

Divisibility Rule For 22

To determine if a number is divisible by 22, we can use the divisibility rules for both 2 and 11, since (22 = 2 x 11).

1. Divisibility Rule for 2:

A number is divisible by 2 if its last digit is even. This means the last digit can be 0, 2, 4, 6, or 8.

2. Divisibility Rule for 11:

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or a multiple of 11.

Steps for the Rule of 11:

1. Identify the digits in odd and even positions.
2. Sum the digits in odd positions and the digits in even positions.
3. Subtract the smaller sum from the larger sum.
4. Check if the result is 0 or divisible by 11.

Combining the Rules for 22:

For a number to be divisible by 22, it must:

• Have an even last digit (for divisibility by 2).
• Pass the test for divisibility by 11.

Examples:

1. Example: 110

• Divisibility by 2:
  • Last digit: 0 (even, so divisible by 2).
• Divisibility by 11:
  • Odd position digits: (1 + 0 = 1)
  • Even position digits: (1)
  • Difference: (1 – 1 = 0) (which is divisible by 11).
• Both conditions are met, so 110 is divisible by 22.

1. Example: 264

• Divisibility by 2:
  • Last digit: 4 (even, so divisible by 2).
• Divisibility by 11:
  • Odd position digits: (2 + 4 = 6)
  • Even position digits: (6)
  • Difference: (6 – 6 = 0) (which is divisible by 11).
• Both conditions are met, so 264 is divisible by 22.

1. Example: 44

• Divisibility by 2:
  • Last digit: 4 (even, so divisible by 2).
• Divisibility by 11:
  • Odd position digits: (4)
  • Even position digits: (4)
  • Difference: (4 – 4 = 0) (which is divisible by 11).
• Both conditions are met, so 44 is divisible by 22.

1. Example: 63

• Divisibility by 2:
  • Last digit: 3 (not even, so not divisible by 2).
• Since it fails the first condition, 63 is not divisible by 22.

1. Example: 220

• Divisibility by 2:
  • Last digit: 0 (even, so divisible by 2).
• Divisibility by 11:
  • Odd position digits: (2 + 0 = 2)
  • Even position digits: (2)
  • Difference: (2 – 2 = 0) (which is divisible by 11).
• Both conditions are met, so 220 is divisible by 22.

Conclusion

To check if a number is divisible by 22:

• Ensure it has an even last digit (for divisibility by 2).
• Verify the difference between the sums of the digits in odd and even positions is 0 or a multiple of 11 (for divisibility by 11).

Both conditions must be satisfied for the number to be divisible by 22.