A six-digit number divisible by 11 is any number between 100,000 and 999,999 that can be divided by 11 without leaving a remainder.
Here's a breakdown:
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Divisibility Rule for 11: A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or divisible by 11. For example, in the number 123,456:
- Sum of digits at odd places: 1 + 3 + 5 = 9
- Sum of digits at even places: 2 + 4 + 6 = 12
- Difference: |9 - 12| = 3. Since 3 is not 0 or divisible by 11, 123,456 is not divisible by 11.
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Examples:
- 100100 is not divisible by 11 because (1+0+0) - (0+1+0) = 0, meaning 100100 is divisible by 11
- 100,110 is divisible by 11: (1 + 0 + 1) - (0 + 1 + 0) = 2 - 1 = 1 which means 100110 is not divisible by 11
- 100,001 is not divisible by 11. The difference in the sums is (1+0+0) - (0+0+1) = 0, so it is divisible by 11!
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Smallest Six-Digit Number Divisible by 11: The smallest six-digit number is 100,000. When you divide 100,000 by 11, you get 9090 with a remainder of 10. This means 100,000 + (11-10) = 100,001 is the smallest six-digit number divisible by 11.
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Largest Six-Digit Number Divisible by 11: The largest six-digit number is 999,999. Dividing 999,999 by 11 gives 90909 with no remainder. Therefore, 999,999 is the largest six-digit number divisible by 11.
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Quantity of Six-Digit Numbers Divisible by 11: There are 81,818 six-digit numbers that are divisible by 11.
