10421202 divided by 586 
We want to figure out the number of times 10421202 can be divided by 586.

Let's proceed to step 1:
586 goes into 1 0 times with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 586

On to step 2:
586 goes into 10 0 times with a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Fetch the next digit (4) from the dividend, attach it to 10 and continue: 104 / 586

On to step 3:
If we divide 104 by 586, we get 0 and a remainder of 104.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 104 after subtracting 0 from 104.
Grab the next digit (2) from the dividend, add it to 104, then carry on: 1042 / 586

Moving on to step 4:
When dividing 1042 by 586, we get 1 with a remainder of 456.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 586 from 1042 to get 456.
Bring next digit (1) of the dividend behind the 456 and repeat the process: 4561 / 586

Advancing to step 5:
586 goes into 4561 7 times with a remainder of 459.
Put 7 as the next digit of the answer. 
Result so far: 17.0
Subtracting 4102 from 4561 leaves us with 459.
Take the next digit (2) from the dividend and append it to 459, then repeat: 4592 / 586

Advancing to step 6:
The number 586 fits into 4592 7 times, leaving a remainder of 490.
The next digit of our result is 7. 
Result so far: 177.0
Deduct 4102 from 4592 and we're left with 490.
Append the next digit (0) from the dividend to 490 and continue with: 4900 / 586

Advancing to step 7:
If we divide 4900 by 586, we get 8 and a remainder of 212.
Put 8 as the next digit of the answer. 
Result so far: 1778.0
Subtracting 4688 from 4900 leaves us with 212.
Grab the next digit (2) from the dividend, add it to 212, then carry on: 2122 / 586

Moving on to step 8:
If we divide 2122 by 586, we get 3 and a remainder of 364.
Use 3 as the next digit of our solution. 
Result so far: 17783.0
If we subtract 1758 from 2122, we get 364.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3640, and continue the process.

On to step 9:
586 goes into 3640 6 times with a remainder of 124.
Put 6 as the next digit of the answer. 
Result so far: 17783.6
Subtract 3516 from 3640 to get 124.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1240, and continue the process.

Going ahead to step 10:
1240 divided by 586 is 2 with a remainder of 68.
Record the quotient 2 as the next digit in the result. 
Result so far: 17783.62
Subtract 1172 from 1240 to get 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Step 11:
The number 586 fits into 680 1 times, leaving a remainder of 94.
Use 1 as the next digit of our solution. 
Result so far: 17783.621
The remainder is 94 after subtracting 586 from 680.
Since there are no more digits in the dividend, we add a zero to the remainder making it 940, and continue the process.

Step 12:
586 goes into 940 1 times with a remainder of 354.
Record the quotient 1 as the next digit in the result. 
Result so far: 17783.6211
Subtracting 586 from 940 leaves us with 354.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3540, and continue the process.

In conclusion, the division gives 17783.6211 with a balance of 0.00354.