We're dividing 738645 by 126 
We're looking to find how many times 126 goes into 738645.

Moving on to step 1:
When dividing 7 by 126, we get 0 with a remainder of 7.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 7 to get 7.
Grab the next digit (3) from the dividend, add it to 7, then carry on: 73 / 126

Moving on to step 2:
73 divided by 126 is 0 with a remainder of 73.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 73, we end up with 73.
Fetch the next digit (8) from the dividend, attach it to 73 and continue: 738 / 126

On to step 3:
The number 126 fits into 738 5 times, leaving a remainder of 108.
The next digit of our result is 5. 
Result so far: 5.0
Subtract 630 from 738 to get 108.
Grab the next digit (6) from the dividend, add it to 108, then carry on: 1086 / 126

Step 4:
When dividing 1086 by 126, we get 8 with a remainder of 78.
Use 8 as the next digit of our solution. 
Result so far: 58.0
The remainder is 78 after subtracting 1008 from 1086.
Append the next digit (4) from the dividend to 78 and continue with: 784 / 126

Let's proceed to step 5:
126 goes into 784 6 times with a remainder of 28.
Write down 6 as next digit of the result. 
Result so far: 586.0
Deduct 756 from 784 and we're left with 28.
Bring next digit (5) of the dividend behind the 28 and repeat the process: 285 / 126

Going ahead to step 6:
If we divide 285 by 126, we get 2 and a remainder of 33.
Put 2 as the next digit of the answer. 
Result so far: 5862.0
The remainder is 33 after subtracting 252 from 285.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Moving on to step 7:
126 goes into 330 2 times with a remainder of 78.
Use 2 as the next digit of our solution. 
Result so far: 5862.2
If we subtract 252 from 330, we get 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Step 8:
When dividing 780 by 126, we get 6 with a remainder of 24.
Record the quotient 6 as the next digit in the result. 
Result so far: 5862.26
If we take 756 away from 780, we end up 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.

Moving on to step 9:
When dividing 240 by 126, we get 1 with a remainder of 114.
The next digit of our result is 1. 
Result so far: 5862.261
Subtracting 126 from 240 leaves us with 114.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1140, and continue the process.

Going ahead to step 10:
The number 126 fits into 1140 9 times, leaving a remainder of 6.
The number 9 becomes the next digit in our result. 
Result so far: 5862.2619
The remainder is 6 after subtracting 1134 from 1140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 11:
126 can be fit into 60 0 times, resulting in a remainder of 60.
Record the quotient 0 as the next digit in the result. 
Result so far: 5862.2619
If we take 0 away from 60, we end up with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

On to step 12:
If we divide 600 by 126, we get 4 and a remainder of 96.
Write down 4 as next digit of the result. 
Result so far: 5862.261904
If we subtract 504 from 600, we get 96.
Since there are no more digits in the dividend, we add a zero to the remainder making it 960, and continue the process.

Going ahead to step 13:
If we divide 960 by 126, we get 7 and a remainder of 78.
Put 7 as the next digit of the answer. 
Result so far: 5862.2619047
If we subtract 882 from 960, we get 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Step 14:
The number 126 fits into 780 6 times, leaving a remainder of 24.
The number 6 becomes the next digit in our result. 
Result so far: 5862.26190476
Subtracting 756 from 780 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.

The final outcome is 5862.26190476, with a leftover of 2.4e-08.