We divide 635674 by 89
We're looking to find how many times 89 goes into 635674.

Advancing to step 1:
When dividing 6 by 89, we get 0 with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 6 and we're left with 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 89

Let's proceed to step 2:
63 divided by 89 is 0 with a remainder of 63.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 63 to get 63.
Grab the next digit (5) from the dividend, add it to 63, then carry on: 635 / 89

Going ahead to step 3:
The number 89 fits into 635 7 times, leaving a remainder of 12.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we subtract 623 from 635, we get 12.
Grab the next digit (6) from the dividend, add it to 12, then carry on: 126 / 89

Moving on to step 4:
If we divide 126 by 89, we get 1 and a remainder of 37.
The next digit of our result is 1. 
Result so far: 71.0
If we subtract 89 from 126, we get 37.
Bring next digit (7) of the dividend behind the 37 and repeat the process: 377 / 89

Advancing to step 5:
377 divided by 89 is 4 with a remainder of 21.
The next digit of our result is 4. 
Result so far: 714.0
The remainder is 21 after subtracting 356 from 377.
Bring next digit (4) of the dividend behind the 21 and repeat the process: 214 / 89

On to step 6:
89 can be fit into 214 2 times, resulting in a remainder of 36.
Put 2 as the next digit of the answer. 
Result so far: 7142.0
If we take 178 away from 214, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 7:
The number 89 fits into 360 4 times, leaving a remainder of 4.
Write down 4 as next digit of the result. 
Result so far: 7142.4
Subtract 356 from 360 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 8:
89 goes into 40 0 times with a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 7142.4
Subtracting 0 from 40 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Moving on to step 9:
400 divided by 89 is 4 with a remainder of 44.
The next digit of our result is 4. 
Result so far: 7142.404
The remainder is 44 after subtracting 356 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Let's proceed to step 10:
If we divide 440 by 89, we get 4 and a remainder of 84.
The next digit of our result is 4. 
Result so far: 7142.4044
Deduct 356 from 440 and we're left with 84.
Since there are no more digits in the dividend, we add a zero to the remainder making it 840, and continue the process.

The final result is 7142.4044 with a remainder of 0.00084.