6100114 ÷ 413 
Our goal is to divide 6100114 by 413.

Moving on to step 1:
When dividing 6 by 413, we get 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Grab the next digit (1) from the dividend, add it to 6, then carry on: 61 / 413

Step 2:
If we divide 61 by 413, we get 0 and a remainder of 61.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 61 leaves us with 61.
Append the next digit (0) from the dividend to 61 and continue with: 610 / 413

Moving on to step 3:
413 can be fit into 610 1 times, resulting in a remainder of 197.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
The remainder is 197 after subtracting 413 from 610.
Append the next digit (0) from the dividend to 197 and continue with: 1970 / 413

Moving on to step 4:
413 can be fit into 1970 4 times, resulting in a remainder of 318.
Record the quotient 4 as the next digit in the result. 
Result so far: 14.0
If we take 1652 away from 1970, we end up with 318.
Append the next digit (1) from the dividend to 318 and continue with: 3181 / 413

Moving on to step 5:
413 goes into 3181 7 times with a remainder of 290.
Write down 7 as next digit of the result. 
Result so far: 147.0
Subtracting 2891 from 3181 leaves us with 290.
Grab the next digit (1) from the dividend, add it to 290, then carry on: 2901 / 413

Moving on to step 6:
413 goes into 2901 7 times with a remainder of 10.
Put 7 as the next digit of the answer. 
Result so far: 1477.0
Deduct 2891 from 2901 and we're left with 10.
Grab the next digit (4) from the dividend, add it to 10, then carry on: 104 / 413

Going ahead to step 7:
104 divided by 413 is 0 with a remainder of 104.
Put 0 as the next digit of the answer. 
Result so far: 14770.0
Subtracting 0 from 104 leaves us with 104.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1040, and continue the process.

Advancing to step 8:
The number 413 fits into 1040 2 times, leaving a remainder of 214.
Put 2 as the next digit of the answer. 
Result so far: 14770.2
Deduct 826 from 1040 and we're left with 214.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2140, and continue the process.

Step 9:
The number 413 fits into 2140 5 times, leaving a remainder of 75.
Write down 5 as next digit of the result. 
Result so far: 14770.25
Subtracting 2065 from 2140 leaves us with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Advancing to step 10:
If we divide 750 by 413, we get 1 and a remainder of 337.
Use 1 as the next digit of our solution. 
Result so far: 14770.251
If we subtract 413 from 750, we get 337.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3370, and continue the process.

Let's proceed to step 11:
The number 413 fits into 3370 8 times, leaving a remainder of 66.
Put 8 as the next digit of the answer. 
Result so far: 14770.2518
If we subtract 3304 from 3370, we get 66.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Going ahead to step 12:
When dividing 660 by 413, we get 1 with a remainder of 247.
Use 1 as the next digit of our solution. 
Result so far: 14770.25181
Deduct 413 from 660 and we're left with 247.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2470, and continue the process.

Let's proceed to step 13:
2470 divided by 413 is 5 with a remainder of 405.
The next digit of our result is 5. 
Result so far: 14770.251815
If we take 2065 away from 2470, we end up with 405.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4050, and continue the process.

Advancing to step 14:
413 goes into 4050 9 times with a remainder of 333.
Record the quotient 9 as the next digit in the result. 
Result so far: 14770.2518159
If we take 3717 away from 4050, we end up with 333.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3330, and continue the process.

Advancing to step 15:
413 goes into 3330 8 times with a remainder of 26.
Write down 8 as next digit of the result. 
Result so far: 14770.25181598
Subtract 3304 from 3330 to get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

In conclusion, the division gives 14770.25181598 with a balance of 2.6e-08.