641586 ÷ 34 
Our goal is to divide 641586 by 34.

Advancing to step 1:
If we divide 6 by 34, we get 0 and a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 34

Advancing to step 2:
When dividing 64 by 34, we get 1 with a remainder of 30.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
The remainder is 30 after subtracting 34 from 64.
Grab the next digit (1) from the dividend, add it to 30, then carry on: 301 / 34

Moving on to step 3:
34 can be fit into 301 8 times, resulting in a remainder of 29.
Record the quotient 8 as the next digit in the result. 
Result so far: 18.0
Subtracting 272 from 301 leaves us with 29.
Append the next digit (5) from the dividend to 29 and continue with: 295 / 34

Advancing to step 4:
295 divided by 34 is 8 with a remainder of 23.
Write down 8 as next digit of the result. 
Result so far: 188.0
Deduct 272 from 295 and we're left with 23.
Fetch the next digit (8) from the dividend, attach it to 23 and continue: 238 / 34

On to step 5:
The number 34 fits into 238 7 times, leaving a remainder of 0.
Write down 7 as next digit of the result. 
Result so far: 1887.0
The remainder is 0 after subtracting 238 from 238.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 34

On to step 6:
34 goes into 6 0 times with a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 18870.0
Subtracting 0 from 6 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 7:
If we divide 60 by 34, we get 1 and a remainder of 26.
Record the quotient 1 as the next digit in the result. 
Result so far: 18870.1
The remainder is 26 after subtracting 34 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Step 8:
If we divide 260 by 34, we get 7 and a remainder of 22.
Record the quotient 7 as the next digit in the result. 
Result so far: 18870.17
The remainder is 22 after subtracting 238 from 260.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 9:
If we divide 220 by 34, we get 6 and a remainder of 16.
Record the quotient 6 as the next digit in the result. 
Result so far: 18870.176
Subtract 204 from 220 to get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 10:
34 can be fit into 160 4 times, resulting in a remainder of 24.
Use 4 as the next digit of our solution. 
Result so far: 18870.1764
If we subtract 136 from 160, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

On to step 11:
240 divided by 34 is 7 with a remainder of 2.
Write down 7 as next digit of the result. 
Result so far: 18870.17647
Deduct 238 from 240 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 12:
20 divided by 34 is 0 with a remainder of 20.
The number 0 becomes the next digit in our result. 
Result so far: 18870.17647
If we take 0 away from 20, we end up with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 13:
If we divide 200 by 34, we get 5 and a remainder of 30.
Record the quotient 5 as the next digit in the result. 
Result so far: 18870.1764705
The remainder is 30 after subtracting 170 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 14:
34 goes into 300 8 times with a remainder of 28.
Record the quotient 8 as the next digit in the result. 
Result so far: 18870.17647058
Subtract 272 from 300 to get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

After the division, we end up with 18870.17647058 and a remainder of 2.8e-08.