We're dividing 546974 by 13 
Our goal is to divide 546974 by 13.

Moving on to step 1:
13 can be fit into 5 0 times, resulting in a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Grab the next digit (4) from the dividend, add it to 5, then carry on: 54 / 13

Advancing to step 2:
13 can be fit into 54 4 times, resulting in a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we subtract 52 from 54, we get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 13

Moving on to step 3:
If we divide 26 by 13, we get 2 and a remainder of 0.
The number 2 becomes the next digit in our result. 
Result so far: 42.0
The remainder is 0 after subtracting 26 from 26.
Take the next digit (9) from the dividend and append it to 0, then repeat: 9 / 13

On to step 4:
13 goes into 9 0 times with a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 420.0
If we take 0 away from 9, we end up with 9.
Take the next digit (7) from the dividend and append it to 9, then repeat: 97 / 13

Advancing to step 5:
When dividing 97 by 13, we get 7 with a remainder of 6.
Use 7 as the next digit of our solution. 
Result so far: 4207.0
If we take 91 away from 97, we end up with 6.
Fetch the next digit (4) from the dividend, attach it to 6 and continue: 64 / 13

Moving on to step 6:
The number 13 fits into 64 4 times, leaving a remainder of 12.
Put 4 as the next digit of the answer. 
Result so far: 42074.0
If we subtract 52 from 64, we get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 7:
When dividing 120 by 13, we get 9 with a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 42074.9
If we subtract 117 from 120, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 8:
13 goes into 30 2 times with a remainder of 4.
Put 2 as the next digit of the answer. 
Result so far: 42074.92
Subtract 26 from 30 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Going ahead to step 9:
13 goes into 40 3 times with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 42074.923
Subtract 39 from 40 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 10:
13 goes into 10 0 times with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 42074.923
If we subtract 0 from 10, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 11:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Record the quotient 7 as the next digit in the result. 
Result so far: 42074.92307
The remainder is 9 after subtracting 91 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 12:
90 divided by 13 is 6 with a remainder of 12.
Write down 6 as next digit of the result. 
Result so far: 42074.923076
Subtract 78 from 90 to get 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 13:
If we divide 120 by 13, we get 9 and a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 42074.9230769
The remainder is 3 after subtracting 117 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 14:
The number 13 fits into 30 2 times, leaving a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 42074.92307692
The remainder is 4 after subtracting 26 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

The quotient of the division is 42074.92307692, and the remainder is 4e-09.