Which of the following numbers are divisible by 11?
1052524

Answer

To determine if the number 1052524 is divisible by 11, we will follow these steps:

### Step 1: Identify the digits and their positions
The number is 1052524. We will identify the positions of each digit:
- 1 (1st position - odd)
- 0 (2nd position - even)
- 5 (3rd position - odd)
- 2 (4th position - even)
- 5 (5th position - odd)
- 2 (6th position - even)
- 4 (7th position - odd)

### Step 2: Sum the digits in odd positions
The digits in odd positions are: 1 (1st), 5 (3rd), 5 (5th), and 4 (7th).
Now, we will calculate the sum:
- Sum of odd positions = 1 + 5 + 5 + 4 = 15

### Step 3: Sum the digits in even positions
The digits in even positions are: 0 (2nd), 2 (4th), and 2 (6th).
Now, we will calculate the sum:
- Sum of even positions = 0 + 2 + 2 = 4

### Step 4: Find the difference between the sums
Now we will find the difference between the sum of the odd positions and the sum of the even positions:
- Difference = Sum of odd positions - Sum of even positions = 15 - 4 = 11

### Step 5: Check if the difference is divisible by 11
According to the divisibility rule for 11, if the difference is 0 or a multiple of 11, then the number is divisible by 11. Here, the difference is 11, which is a multiple of 11.

### Conclusion
Since the difference is a multiple of 11, we conclude that the number 1052524 is divisible by 11.

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