We look at the division of 35495638 by 677 
We want to figure out the number of times 35495638 can be divided by 677.

Advancing to step 1:
3 divided by 677 is 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Fetch the next digit (5) from the dividend, attach it to 3 and continue: 35 / 677

Moving on to step 2:
When dividing 35 by 677, we get 0 with a remainder of 35.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 35 after subtracting 0 from 35.
Include the next digit (4) from the dividend after 35, then repeat: 354 / 677

Moving on to step 3:
354 divided by 677 is 0 with a remainder of 354.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 354 leaves us with 354.
Bring next digit (9) of the dividend behind the 354 and repeat the process: 3549 / 677

Going ahead to step 4:
677 goes into 3549 5 times with a remainder of 164.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Subtracting 3385 from 3549 leaves us with 164.
Take the next digit (5) from the dividend and append it to 164, then repeat: 1645 / 677

Let's proceed to step 5:
If we divide 1645 by 677, we get 2 and a remainder of 291.
Use 2 as the next digit of our solution. 
Result so far: 52.0
If we subtract 1354 from 1645, we get 291.
Take the next digit (6) from the dividend and append it to 291, then repeat: 2916 / 677

On to step 6:
If we divide 2916 by 677, we get 4 and a remainder of 208.
The number 4 becomes the next digit in our result. 
Result so far: 524.0
If we subtract 2708 from 2916, we get 208.
Include the next digit (3) from the dividend after 208, then repeat: 2083 / 677

Let's proceed to step 7:
677 goes into 2083 3 times with a remainder of 52.
The number 3 becomes the next digit in our result. 
Result so far: 5243.0
If we take 2031 away from 2083, we end up with 52.
Include the next digit (8) from the dividend after 52, then repeat: 528 / 677

On to step 8:
The number 677 fits into 528 0 times, leaving a remainder of 528.
Put 0 as the next digit of the answer. 
Result so far: 52430.0
Subtracting 0 from 528 leaves us with 528.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5280, and continue the process.

Advancing to step 9:
5280 divided by 677 is 7 with a remainder of 541.
Record the quotient 7 as the next digit in the result. 
Result so far: 52430.7
Subtracting 4739 from 5280 leaves us with 541.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5410, and continue the process.

On to step 10:
677 goes into 5410 7 times with a remainder of 671.
Put 7 as the next digit of the answer. 
Result so far: 52430.77
Deduct 4739 from 5410 and we're left with 671.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6710, and continue the process.

The final result is 52430.77 with a remainder of 0.671.