Let's divide 415742 by 13
We're looking to find how many times 13 goes into 415742.

Going ahead to step 1:
4 divided by 13 is 0 with a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 4 and we're left with 4.
Append the next digit (1) from the dividend to 4 and continue with: 41 / 13

Moving on to step 2:
13 can be fit into 41 3 times, resulting in a remainder of 2.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Subtracting 39 from 41 leaves us with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 13

Moving on to step 3:
13 can be fit into 25 1 times, resulting in a remainder of 12.
Use 1 as the next digit of our solution. 
Result so far: 31.0
The remainder is 12 after subtracting 13 from 25.
Append the next digit (7) from the dividend to 12 and continue with: 127 / 13

Going ahead to step 4:
When dividing 127 by 13, we get 9 with a remainder of 10.
Put 9 as the next digit of the answer. 
Result so far: 319.0
Subtract 117 from 127 to get 10.
Append the next digit (4) from the dividend to 10 and continue with: 104 / 13

Let's proceed to step 5:
The number 13 fits into 104 8 times, leaving a remainder of 0.
Record the quotient 8 as the next digit in the result. 
Result so far: 3198.0
If we subtract 104 from 104, we get 0.
Take the next digit (2) from the dividend and append it to 0, then repeat: 2 / 13

Advancing to step 6:
If we divide 2 by 13, we get 0 and a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 31980.0
Deduct 0 from 2 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:
13 can be fit into 20 1 times, resulting in a remainder of 7.
The next digit of our result is 1. 
Result so far: 31980.1
The remainder is 7 after subtracting 13 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 8:
13 goes into 70 5 times with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 31980.15
If we take 65 away from 70, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 9:
50 divided by 13 is 3 with a remainder of 11.
Put 3 as the next digit of the answer. 
Result so far: 31980.153
If we take 39 away from 50, we end up with 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Going ahead to step 10:
13 goes into 110 8 times with a remainder of 6.
Put 8 as the next digit of the answer. 
Result so far: 31980.1538
If we take 104 away from 110, we end up with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 11:
The number 13 fits into 60 4 times, leaving a remainder of 8.
Put 4 as the next digit of the answer. 
Result so far: 31980.15384
If we take 52 away from 60, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 12:
When dividing 80 by 13, we get 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 31980.153846
The remainder is 2 after subtracting 78 from 80.
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 13:
When dividing 20 by 13, we get 1 with a remainder of 7.
The number 1 becomes the next digit in our result. 
Result so far: 31980.1538461
If we subtract 13 from 20, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 14:
13 goes into 70 5 times with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 31980.15384615
The remainder is 5 after subtracting 65 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The final result is 31980.15384615 with a remainder of 5e-09.