Short Answer 
The long number ‘147’ is repeated 841 times, leading to a total digit sum of 10092. When divided by 11, the remainder is 5.
Step 1: Understanding the Number
To begin solving the problem, recognize that the long number consists of the digits ‘147’ repeated 841 times. This means we should treat it as one continuous sequence: 147147147… for a total of 841 repetitions. Understanding this structure helps us simplify the calculations we need to perform.
Step 2: Finding the Sum of Digits
Next, apply the divisibility rule for 11 by first calculating the sum of the digits in ‘147’. The digits are:
- 1
- 4
- 7
Sum these digits: 1 + 4 + 7 = 12. Since the digits of ‘147’ repeat 841 times, the total sum of all the digits will be: 12 ‚à öo 841 = 10092.
Step 3: Calculating the Remainder with 11
Finally, to find the remainder when 10092 is divided by 11, perform the division: 10092 ‚à ö‚à ë 11 = 917 with some remainder. Calculate the whole part: 917 ‚à öo 11 = 10087. The remainder is then found by subtracting: 10092 – 10087 = 5. Thus, the remainder when the number is divided by 11 is 5.