Examine the following numbers for divisibility by 11:
7136985

Answer

To determine if the number 7136985 is divisible by 11, we will follow the divisibility rule for 11. According to this rule, we need to find the difference between the sum of the digits in odd positions and the sum of the digits in even positions. If this difference is 0 or a multiple of 11, then the number is divisible by 11.

### Step-by-Step Solution:

1. **Identify the Positions of the Digits**:
We will number the digits of the number from right to left:
- 5 (1st position)
- 8 (2nd position)
- 9 (3rd position)
- 6 (4th position)
- 3 (5th position)
- 7 (6th position)
- 1 (7th position)

2. **Sum of Digits at Odd Positions**:
The digits in the odd positions are: 5 (1st), 9 (3rd), 3 (5th), and 7 (7th).
- Sum = 5 + 9 + 3 + 7
- Sum = 24

3. **Sum of Digits at Even Positions**:
The digits in the even positions are: 8 (2nd), 6 (4th), and 1 (6th).
- Sum = 8 + 6 + 1
- Sum = 15

4. **Calculate the Difference**:
Now, we will find the difference between the sum of the digits at odd positions and the sum of the digits at even positions.
- Difference = Sum of odd positions - Sum of even positions
- Difference = 24 - 15
- Difference = 9

5. **Check the Result**:
We need to check if the difference (9) is either 0 or a multiple of 11.
- Since 9 is neither 0 nor a multiple of 11, we conclude that the number 7136985 is **not divisible by 11**.

### Final Conclusion:
The number 7136985 is not divisible by 11.

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