135974 ÷ 44 
We want to figure out the number of times 135974 can be divided by 44.

Advancing to step 1:
1 divided by 44 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 44

On to step 2:
13 divided by 44 is 0 with a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 13 to get 13.
Append the next digit (5) from the dividend to 13 and continue with: 135 / 44

Advancing to step 3:
The number 44 fits into 135 3 times, leaving a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 3.0
Deduct 132 from 135 and we're left with 3.
Fetch the next digit (9) from the dividend, attach it to 3 and continue: 39 / 44

Step 4:
44 can be fit into 39 0 times, resulting in a remainder of 39.
Use 0 as the next digit of our solution. 
Result so far: 30.0
If we take 0 away from 39, we end up with 39.
Bring next digit (7) of the dividend behind the 39 and repeat the process: 397 / 44

Advancing to step 5:
397 divided by 44 is 9 with a remainder of 1.
Write down 9 as next digit of the result. 
Result so far: 309.0
If we subtract 396 from 397, we get 1.
Append the next digit (4) from the dividend to 1 and continue with: 14 / 44

Going ahead to step 6:
44 can be fit into 14 0 times, resulting in a remainder of 14.
The next digit of our result is 0. 
Result so far: 3090.0
Deduct 0 from 14 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.

Let's proceed to step 7:
The number 44 fits into 140 3 times, leaving a remainder of 8.
Use 3 as the next digit of our solution. 
Result so far: 3090.3
Subtracting 132 from 140 leaves us 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.

Going ahead to step 8:
44 can be fit into 80 1 times, resulting in a remainder of 36.
The next digit of our result is 1. 
Result so far: 3090.31
If we take 44 away from 80, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 9:
360 divided by 44 is 8 with a remainder of 8.
Use 8 as the next digit of our solution. 
Result so far: 3090.318
Subtract 352 from 360 to get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 10:
When dividing 80 by 44, we get 1 with a remainder of 36.
Write down 1 as next digit of the result. 
Result so far: 3090.3181
If we take 44 away from 80, we end up with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Going ahead to step 11:
44 can be fit into 360 8 times, resulting in a remainder of 8.
The number 8 becomes the next digit in our result. 
Result so far: 3090.31818
Deduct 352 from 360 and we're left 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.

Going ahead to step 12:
If we divide 80 by 44, we get 1 and a remainder of 36.
Record the quotient 1 as the next digit in the result. 
Result so far: 3090.318181
If we subtract 44 from 80, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Moving on to step 13:
The number 44 fits into 360 8 times, leaving a remainder of 8.
Write down 8 as next digit of the result. 
Result so far: 3090.3181818
Deduct 352 from 360 and we're left 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.

Let's proceed to step 14:
The number 44 fits into 80 1 times, leaving a remainder of 36.
The next digit of our result is 1. 
Result so far: 3090.31818181
Subtracting 44 from 80 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

The quotient of the division is 3090.31818181, and the remainder is 3.6e-08.