Short Answer 
The number ‘147’ repeated 841 times has a total digit sum of 10092. When 10092 is divided by 11, the remainder is found to be 5.
Step 1: Understand the Number Formation
The number formed by writing ‘147’ 841 times can be visualized as a long sequence of numbers: 147147147… up to 841 repetitions. This means we are essentially dealing with the digit sequence ‘147’ repeated multiple times, which will help us in calculating the total value and its behavior under division.
Step 2: Calculate the Sum of the Digits
To determine the remainder when this large number is divided by 11, we follow the divisibility rule for 11, which relies on the digit sums. The digits of ‘147’ are:
- 1
- 4
- 7
The sum of these digits is calculated as follows: 1 + 4 + 7 = 12. Since ‘147’ is repeated 841 times, the total sum of the digits is 12 multiplied by 841, resulting in 10092.
Step 3: Find the Remainder When Divided by 11
Now that we have the total sum of digits (10092), the next step is to find the remainder when this sum is divided by 11. We perform the division:
- 10092 √∑ 11 = 917
- Calculating: 917 √ó 11 = 10087
The remainder is then found by subtracting: 10092 – 10087 = 5. Therefore, the remainder when the large number is divided by 11 is 5.