The number 58129745812974 is divisible by

Options

A. 11
B. 9
C. 4
D. None of these

Answer

To determine if the number 58129745812974 is divisible by 11, we can follow these steps:

### Step 1: Identify the digits of the number
The number is 58129745812974. We will break it down into its individual digits:
- 5, 8, 1, 2, 9, 7, 4, 5, 8, 1, 2, 9, 7, 4

### Step 2: Apply the divisibility rule for 11
The rule states that a number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is either 0 or divisible by 11.

### Step 3: Sum the digits in odd positions
The digits in odd positions (1st, 3rd, 5th, etc.) are:
- 5 (1st)
- 1 (3rd)
- 9 (5th)
- 7 (7th)
- 8 (9th)
- 2 (11th)
- 7 (13th)

Calculating the sum:
\[ 5 + 1 + 9 + 7 + 8 + 2 + 7 = 39 \]

### Step 4: Sum the digits in even positions
The digits in even positions (2nd, 4th, 6th, etc.) are:
- 8 (2nd)
- 2 (4th)
- 7 (6th)
- 5 (8th)
- 1 (10th)
- 9 (12th)
- 4 (14th)

Calculating the sum:
\[ 8 + 2 + 7 + 5 + 1 + 9 + 4 = 36 \]

### Step 5: Find the difference between the two sums
Now we find the difference between the sum of the odd-positioned digits and the sum of the even-positioned digits:
\[ 39 - 36 = 3 \]

### Step 6: Check if the difference is divisible by 11
The difference is 3, which is not divisible by 11.

### Conclusion
Since the difference is not 0 or divisible by 11, we conclude that the number 58129745812974 is **not divisible by 11**.

---