We divide 377633 by 3
We're looking to find how many times 3 goes into 377633.

Moving on to step 1:
3 divided by 3 is 1 with a remainder of 0.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 3 from 3, we get 0.
Append the next digit (7) from the dividend to 0 and continue with: 7 / 3

Going ahead to step 2:
If we divide 7 by 3, we get 2 and a remainder of 1.
Use 2 as the next digit of our solution. 
Result so far: 12.0
Deduct 6 from 7 and we're left with 1.
Take the next digit (7) from the dividend and append it to 1, then repeat: 17 / 3

Advancing to step 3:
17 divided by 3 is 5 with a remainder of 2.
Write down 5 as next digit of the result. 
Result so far: 125.0
Subtract 15 from 17 to get 2.
Fetch the next digit (6) from the dividend, attach it to 2 and continue: 26 / 3

On to step 4:
3 goes into 26 8 times with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 1258.0
Deduct 24 from 26 and we're left with 2.
Take the next digit (3) from the dividend and append it to 2, then repeat: 23 / 3

Advancing to step 5:
23 divided by 3 is 7 with a remainder of 2.
Write down 7 as next digit of the result. 
Result so far: 12587.0
If we subtract 21 from 23, we get 2.
Grab the next digit (3) from the dividend, add it to 2, then carry on: 23 / 3

Going ahead to step 6:
3 goes into 23 7 times with a remainder of 2.
Write down 7 as next digit of the result. 
Result so far: 125877.0
If we take 21 away from 23, we end up 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 7:
20 divided by 3 is 6 with a remainder of 2.
The next digit of our result is 6. 
Result so far: 125877.6
If we subtract 18 from 20, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 8:
3 goes into 20 6 times with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 125877.66
Deduct 18 from 20 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.

In conclusion, the division gives 125877.66 with a balance of 0.002.