357674 divided by 3 
We're looking to find how many times 3 goes into 357674.

Advancing to step 1:
The number 3 fits into 3 1 times, leaving a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 3 from 3 leaves us with 0.
Append the next digit (5) from the dividend to 0 and continue with: 5 / 3

Going ahead to step 2:
When dividing 5 by 3, we get 1 with a remainder of 2.
Use 1 as the next digit of our solution. 
Result so far: 11.0
Subtract 3 from 5 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 3

Let's proceed to step 3:
27 divided by 3 is 9 with a remainder of 0.
Put 9 as the next digit of the answer. 
Result so far: 119.0
If we subtract 27 from 27, we get 0.
Fetch the next digit (6) from the dividend, attach it to 0 and continue: 6 / 3

Moving on to step 4:
The number 3 fits into 6 2 times, leaving a remainder of 0.
Write down 2 as next digit of the result. 
Result so far: 1192.0
The remainder is 0 after subtracting 6 from 6.
Fetch the next digit (7) from the dividend, attach it to 0 and continue: 7 / 3

Let's proceed to step 5:
3 can be fit into 7 2 times, resulting in a remainder of 1.
Record the quotient 2 as the next digit in the result. 
Result so far: 11922.0
Deduct 6 from 7 and we're left with 1.
Grab the next digit (4) from the dividend, add it to 1, then carry on: 14 / 3

Let's proceed to step 6:
When dividing 14 by 3, we get 4 with a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 119224.0
Deduct 12 from 14 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.

Let's proceed to step 7:
If we divide 20 by 3, we get 6 and a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 119224.6
The remainder is 2 after subtracting 18 from 20.
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 can be fit into 20 6 times, resulting in a remainder of 2.
Record the quotient 6 as the next digit in the result. 
Result so far: 119224.66
Subtracting 18 from 20 leaves us 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 119224.66 with a balance of 0.002.