We look at the division of 378598 by 59 
Our goal is to divide 378598 by 59.

On to step 1:
If we divide 3 by 59, we get 0 and a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 3 leaves us with 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 59

On to step 2:
When dividing 37 by 59, we get 0 with a remainder of 37.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 37 to get 37.
Fetch the next digit (8) from the dividend, attach it to 37 and continue: 378 / 59

On to step 3:
59 goes into 378 6 times with a remainder of 24.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we take 354 away from 378, we end up with 24.
Include the next digit (5) from the dividend after 24, then repeat: 245 / 59

Step 4:
245 divided by 59 is 4 with a remainder of 9.
Put 4 as the next digit of the answer. 
Result so far: 64.0
Subtracting 236 from 245 leaves us with 9.
Bring next digit (9) of the dividend behind the 9 and repeat the process: 99 / 59

Advancing to step 5:
99 divided by 59 is 1 with a remainder of 40.
The number 1 becomes the next digit in our result. 
Result so far: 641.0
Subtracting 59 from 99 leaves us with 40.
Grab the next digit (8) from the dividend, add it to 40, then carry on: 408 / 59

Let's proceed to step 6:
59 goes into 408 6 times with a remainder of 54.
Use 6 as the next digit of our solution. 
Result so far: 6416.0
If we subtract 354 from 408, we get 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Step 7:
59 can be fit into 540 9 times, resulting in a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 6416.9
Deduct 531 from 540 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 8:
When dividing 90 by 59, we get 1 with a remainder of 31.
Use 1 as the next digit of our solution. 
Result so far: 6416.91
The remainder is 31 after subtracting 59 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 9:
When dividing 310 by 59, we get 5 with a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 6416.915
Subtract 295 from 310 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

On to step 10:
59 can be fit into 150 2 times, resulting in a remainder of 32.
The number 2 becomes the next digit in our result. 
Result so far: 6416.9152
If we subtract 118 from 150, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 11:
59 goes into 320 5 times with a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 6416.91525
Deduct 295 from 320 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 12:
59 can be fit into 250 4 times, resulting in a remainder of 14.
The number 4 becomes the next digit in our result. 
Result so far: 6416.915254
Deduct 236 from 250 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 13:
59 goes into 140 2 times with a remainder of 22.
The number 2 becomes the next digit in our result. 
Result so far: 6416.9152542
If we subtract 118 from 140, we get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 14:
The number 59 fits into 220 3 times, leaving a remainder of 43.
Use 3 as the next digit of our solution. 
Result so far: 6416.91525423
Deduct 177 from 220 and we're left with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

After the division, we end up with 6416.91525423 and a remainder of 4.3e-08.