Short Answer 
The number is formed by repeating ‘147’ a total of 841 times, leading to a digit analysis where odd indexed digits contribute a total of 6728 and the even indexed digit contributes 3364. The difference is 3364, and when this is divided by 11, the remainder is 9.
Step 1: Understanding the Number Formation
The number in question is created by concatenating the digits ‘147’ for a total of 841 times. This can be mathematically expressed as:
- N = 147147…147 (with ‘147’ repeated 841 times)
This formation means we need to analyze the digits across all repetitions to find a pattern and simplify our calculations when we evaluate this large number.
Step 2: Digit Contributions from Each Block
When analyzing the contributions from the individual digits in each block of ‘147’, we recognize the following:
- Odd indexed digits in ‘147’: 1 and 7 contribute a sum of 8.
- Even indexed digit in ‘147’: 4 contributes a sum of 4.
Since we have 841 sets of ‘147’, we calculate the total contributions by multiplying the contributions per set by the number of sets to find the overall sums.
Step 3: Final Calculation and Remainder
To find the remainder when divided by 11, we first need the difference between the total contributions from odd and even positions:
- Total from odd positions: 6728 (841 sets ‚à öo 8)
- Total from even positions: 3364 (841 sets ‚à öo 4)
Calculating the difference gives us 3364. Finally, when dividing 3364 by 11, the result is 305 with a remainder of 9. Thus, the remainder when dividing the large number by 11 is 9.