13774 divided by 32 
We want to figure out the number of times 13774 can be divided by 32.

Let's proceed to step 1:
32 can be fit into 1 0 times, resulting in a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 32

On to step 2:
If we divide 13 by 32, we get 0 and a remainder of 13.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 13, we get 13.
Fetch the next digit (7) from the dividend, attach it to 13 and continue: 137 / 32

Going ahead to step 3:
137 divided by 32 is 4 with a remainder of 9.
Put 4 as the next digit of the answer. 
Result so far: 4.0
If we take 128 away from 137, we end up with 9.
Take the next digit (7) from the dividend and append it to 9, then repeat: 97 / 32

Advancing to step 4:
If we divide 97 by 32, we get 3 and a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 43.0
The remainder is 1 after subtracting 96 from 97.
Fetch the next digit (4) from the dividend, attach it to 1 and continue: 14 / 32

On to step 5:
32 goes into 14 0 times with a remainder of 14.
The number 0 becomes the next digit in our result. 
Result so far: 430.0
Subtract 0 from 14 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 6:
140 divided by 32 is 4 with a remainder of 12.
Use 4 as the next digit of our solution. 
Result so far: 430.4
If we subtract 128 from 140, 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.

Step 7:
The number 32 fits into 120 3 times, leaving a remainder of 24.
Use 3 as the next digit of our solution. 
Result so far: 430.43
The remainder is 24 after subtracting 96 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 8:
The number 32 fits into 240 7 times, leaving a remainder of 16.
Put 7 as the next digit of the answer. 
Result so far: 430.437
If we take 224 away from 240, we end up with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 9:
32 goes into 160 5 times with a remainder of 0.
Use 5 as the next digit of our solution. 
Result so far: 430.4375
Subtracting 160 from 160 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 10:
32 can be fit into 0 0 times, resulting in a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 430.4375
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 11:
When dividing 0 by 32, we get 0 with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 430.4375
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 430.4375 with a balance of 0.0.