102194 ÷ 13 
We want to figure out the number of times 102194 can be divided by 13.

Moving on to step 1:
13 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 13

Moving on to step 2:
10 divided by 13 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 10, we end up with 10.
Append the next digit (2) from the dividend to 10 and continue with: 102 / 13

Advancing to step 3:
13 goes into 102 7 times with a remainder of 11.
Write down 7 as next digit of the result. 
Result so far: 7.0
Deduct 91 from 102 and we're left with 11.
Grab the next digit (1) from the dividend, add it to 11, then carry on: 111 / 13

Advancing to step 4:
13 can be fit into 111 8 times, resulting in a remainder of 7.
Put 8 as the next digit of the answer. 
Result so far: 78.0
The remainder is 7 after subtracting 104 from 111.
Append the next digit (9) from the dividend to 7 and continue with: 79 / 13

Moving on to step 5:
13 goes into 79 6 times with a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 786.0
If we take 78 away from 79, we end up with 1.
Grab the next digit (4) from the dividend, add it to 1, then carry on: 14 / 13

Advancing to step 6:
14 divided by 13 is 1 with a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 7861.0
Subtract 13 from 14 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.

Let's proceed to step 7:
When dividing 10 by 13, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 7861.0
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 8:
When dividing 100 by 13, we get 7 with a remainder of 9.
Use 7 as the next digit of our solution. 
Result so far: 7861.07
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 9:
13 goes into 90 6 times with a remainder of 12.
The number 6 becomes the next digit in our result. 
Result so far: 7861.076
Subtracting 78 from 90 leaves us with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Advancing to step 10:
13 can be fit into 120 9 times, resulting in a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 7861.0769
If we take 117 away from 120, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 11:
13 can be fit into 30 2 times, resulting in a remainder of 4.
Write down 2 as next digit of the result. 
Result so far: 7861.07692
If we take 26 away from 30, we end up with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 12:
13 goes into 40 3 times with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 7861.076923
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.

Let's proceed to step 13:
If we divide 10 by 13, we get 0 and a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 7861.076923
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.

Advancing to step 14:
13 can be fit into 100 7 times, resulting in a remainder of 9.
Put 7 as the next digit of the answer. 
Result so far: 7861.07692307
If we subtract 91 from 100, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

The quotient of the division is 7861.07692307, and the remainder is 9e-09.