What Is It Divisibility Rules for 4, 8, 11, and 12 Here are examples of numbers that are divisible by 4, 8, 11 and 12. Numbers Divisible by 4 8 11 12 28 32 33 48 812 96 242 180 124 176 495 240 2020 200 253 732
The Correct Answer and Explanation is:
Divisibility Rules for 4, 8, 11, and 12:
1. Divisibility by 4:
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
- Example:
- 28 → The last two digits are 28. Since 28 ÷ 4 = 7, 28 is divisible by 4.
- 32 → The last two digits are 32. Since 32 ÷ 4 = 8, 32 is divisible by 4.
- 812 → The last two digits are 12. Since 12 ÷ 4 = 3, 812 is divisible by 4.
2. Divisibility by 8:
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
- Example:
- 32 → The last three digits are 32. Since 32 ÷ 8 = 4, 32 is divisible by 8.
- 96 → The last three digits are 96. Since 96 ÷ 8 = 12, 96 is divisible by 8.
- 200 → The last three digits are 200. Since 200 ÷ 8 = 25, 200 is divisible by 8.
3. Divisibility by 11:
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11.
- Example:
- 33 → Sum of odd positions = 3, Sum of even positions = 3. Difference = 3 – 3 = 0, which is divisible by 11.
- 242 → Sum of odd positions = 2 + 2 = 4, Sum of even positions = 4. Difference = 4 – 4 = 0, which is divisible by 11.
- 495 → Sum of odd positions = 4 + 5 = 9, Sum of even positions = 9. Difference = 9 – 9 = 0, which is divisible by 11.
4. Divisibility by 12:
A number is divisible by 12 if it is divisible by both 3 and 4.
- Divisibility by 3: The sum of the digits must be divisible by 3.
- Divisibility by 4: The number formed by the last two digits must be divisible by 4.
- Example:
- 48 → Sum of digits = 4 + 8 = 12 (divisible by 3), and the last two digits are 48 (divisible by 4), so 48 is divisible by 12.
- 180 → Sum of digits = 1 + 8 + 0 = 9 (divisible by 3), and the last two digits are 80 (divisible by 4), so 180 is divisible by 12.
- 240 → Sum of digits = 2 + 4 + 0 = 6 (divisible by 3), and the last two digits are 40 (divisible by 4), so 240 is divisible by 12.
In summary, divisibility by 4 is determined by checking the last two digits, divisibility by 8 is determined by checking the last three digits, divisibility by 11 follows the alternating sum rule, and divisibility by 12 requires the number to be divisible by both 3 and 4.
