Which of the following numbers are divisible by 11?
1105645

Answer

To determine whether the number 1105645 is divisible by 11, we will follow the divisibility rule for 11 step by step.

### Step 1: Identify the positions of the digits
The number 1105645 has the following digits:
- 1 (1st position, odd)
- 1 (2nd position, even)
- 0 (3rd position, odd)
- 5 (4th position, even)
- 6 (5th position, odd)
- 4 (6th position, even)
- 5 (7th position, odd)

### Step 2: Sum the digits in the odd positions
The digits in the odd positions are:
- 1 (1st position)
- 0 (3rd position)
- 6 (5th position)
- 5 (7th position)

Now, we calculate the sum:
1 + 0 + 6 + 5 = 12

### Step 3: Sum the digits in the even positions
The digits in the even positions are:
- 1 (2nd position)
- 5 (4th position)
- 4 (6th position)

Now, we calculate the sum:
1 + 5 + 4 = 10

### Step 4: Calculate the difference between the sums
Now, we find the difference between the sum of the odd positions and the sum of the even positions:
12 (sum of odd positions) - 10 (sum of even positions) = 2

### Step 5: Check the divisibility condition
According to the rule, if the difference is 0 or a multiple of 11, then the number is divisible by 11. In this case, the difference is 2, which is neither 0 nor a multiple of 11.

### Conclusion
Thus, the number 1105645 is **not divisible by 11**.

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