We're dividing 169381 by 16 
We're looking to find how many times 16 goes into 169381.

Step 1:
16 goes into 1 0 times with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (6) from the dividend, attach it to 1 and continue: 16 / 16

On to step 2:
When dividing 16 by 16, we get 1 with a remainder of 0.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we take 16 away from 16, we end up with 0.
Append the next digit (9) from the dividend to 0 and continue with: 9 / 16

Advancing to step 3:
16 can be fit into 9 0 times, resulting in a remainder of 9.
Put 0 as the next digit of the answer. 
Result so far: 10.0
Deduct 0 from 9 and we're left with 9.
Bring next digit (3) of the dividend behind the 9 and repeat the process: 93 / 16

On to step 4:
If we divide 93 by 16, we get 5 and a remainder of 13.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
The remainder is 13 after subtracting 80 from 93.
Take the next digit (8) from the dividend and append it to 13, then repeat: 138 / 16

Step 5:
16 can be fit into 138 8 times, resulting in a remainder of 10.
Record the quotient 8 as the next digit in the result. 
Result so far: 1058.0
Subtracting 128 from 138 leaves us with 10.
Grab the next digit (1) from the dividend, add it to 10, then carry on: 101 / 16

On to step 6:
16 can be fit into 101 6 times, resulting in a remainder of 5.
Record the quotient 6 as the next digit in the result. 
Result so far: 10586.0
Deduct 96 from 101 and we're left 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.

Let's proceed to step 7:
When dividing 50 by 16, we get 3 with a remainder of 2.
Use 3 as the next digit of our solution. 
Result so far: 10586.3
If we subtract 48 from 50, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 8:
When dividing 20 by 16, we get 1 with a remainder of 4.
The next digit of our result is 1. 
Result so far: 10586.31
If we subtract 16 from 20, we 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:
If we divide 40 by 16, we get 2 and a remainder of 8.
The next digit of our result is 2. 
Result so far: 10586.312
Subtract 32 from 40 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.

Let's proceed to step 10:
If we divide 80 by 16, we get 5 and a remainder of 0.
The next digit of our result is 5. 
Result so far: 10586.3125
Deduct 80 from 80 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.

Step 11:
If we divide 0 by 16, we get 0 and a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 10586.3125
Subtracting 0 from 0 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.

Let's proceed to step 12:
0 divided by 16 is 0 with a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 10586.3125
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.

The quotient of the division is 10586.3125, and the remainder is 0.0.