We divide 377635 by 31
Our goal is to divide 377635 by 31.

Advancing to step 1:
The number 31 fits into 3 0 times, leaving a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Include the next digit (7) from the dividend after 3, then repeat: 37 / 31

Going ahead to step 2:
If we divide 37 by 31, we get 1 and a remainder of 6.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Deduct 31 from 37 and we're left with 6.
Take the next digit (7) from the dividend and append it to 6, then repeat: 67 / 31

Step 3:
67 divided by 31 is 2 with a remainder of 5.
Use 2 as the next digit of our solution. 
Result so far: 12.0
Deduct 62 from 67 and we're left with 5.
Take the next digit (6) from the dividend and append it to 5, then repeat: 56 / 31

Moving on to step 4:
56 divided by 31 is 1 with a remainder of 25.
The next digit of our result is 1. 
Result so far: 121.0
Subtract 31 from 56 to get 25.
Append the next digit (3) from the dividend to 25 and continue with: 253 / 31

Step 5:
31 can be fit into 253 8 times, resulting in a remainder of 5.
Use 8 as the next digit of our solution. 
Result so far: 1218.0
The remainder is 5 after subtracting 248 from 253.
Fetch the next digit (5) from the dividend, attach it to 5 and continue: 55 / 31

Moving on to step 6:
When dividing 55 by 31, we get 1 with a remainder of 24.
Write down 1 as next digit of the result. 
Result so far: 12181.0
Subtracting 31 from 55 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 7:
The number 31 fits into 240 7 times, leaving a remainder of 23.
The next digit of our result is 7. 
Result so far: 12181.7
If we take 217 away from 240, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 8:
230 divided by 31 is 7 with a remainder of 13.
The next digit of our result is 7. 
Result so far: 12181.77
Subtracting 217 from 230 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

The quotient of the division is 12181.77, and the remainder is 0.013.