Without performing actual division, find the remainder when 28735429 is divided by 11.

Options

A. 5
B. 6
C. 7
D. 8

Answer

To find the remainder when 28735429 is divided by 11 without performing actual division, we can use the divisibility rule for 11. Here’s a step-by-step solution:

### Step 1: Identify the digits and their positions
The number is 28735429. We will identify the positions of the digits:
- Odd positions: 1st (2), 3rd (7), 5th (5), 7th (2)
- Even positions: 2nd (8), 4th (3), 6th (4), 8th (9)

### Step 2: Calculate the sum of the digits at odd positions
Now, we will sum the digits at the odd positions:
- Sum of odd positions = 2 + 7 + 5 + 2 = 16

### Step 3: Calculate the sum of the digits at even positions
Next, we will sum the digits at the even positions:
- Sum of even positions = 8 + 3 + 4 + 9 = 24

### Step 4: Find the difference between the two sums
Now, we will find the difference between the sum of the odd position digits and the sum of the even position digits:
- Difference = Sum of odd positions - Sum of even positions = 16 - 24 = -8

### Step 5: Calculate the modulus of the difference
To find the remainder, we take the modulus of the difference:
- Modulus of -8 = | -8 | = 8

### Step 6: Determine the remainder when divided by 11
Since 8 is less than 11, the remainder when 28735429 is divided by 11 is:
- Remainder = 8

Thus, the remainder when 28735429 is divided by 11 is **8**.

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