We're dividing 59569 by 16 
We're looking to find how many times 16 goes into 59569.

Advancing to step 1:
5 divided by 16 is 0 with a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (9) from the dividend after 5, then repeat: 59 / 16

Going ahead to step 2:
16 goes into 59 3 times with a remainder of 11.
Use 3 as the next digit of our solution. 
Result so far: 3.0
Subtracting 48 from 59 leaves us with 11.
Take the next digit (5) from the dividend and append it to 11, then repeat: 115 / 16

Going ahead to step 3:
If we divide 115 by 16, we get 7 and a remainder of 3.
Use 7 as the next digit of our solution. 
Result so far: 37.0
If we take 112 away from 115, we end up with 3.
Fetch the next digit (6) from the dividend, attach it to 3 and continue: 36 / 16

Going ahead to step 4:
The number 16 fits into 36 2 times, leaving a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 372.0
If we take 32 away from 36, we end up with 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 16

Step 5:
When dividing 49 by 16, we get 3 with a remainder of 1.
The number 3 becomes the next digit in our result. 
Result so far: 3723.0
If we subtract 48 from 49, we 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 6:
The number 16 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 3723.0
Deduct 0 from 10 and we're left 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.

Advancing to step 7:
16 can be fit into 100 6 times, resulting in a remainder of 4.
The next digit of our result is 6. 
Result so far: 3723.06
Subtract 96 from 100 to 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.

Step 8:
The number 16 fits into 40 2 times, leaving a remainder of 8.
The next digit of our result is 2. 
Result so far: 3723.062
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.

Advancing to step 9:
16 can be fit into 80 5 times, resulting in a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 3723.0625
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.

On to step 10:
When dividing 0 by 16, we get 0 with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 3723.0625
The remainder is 0 after subtracting 0 from 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 11:
16 goes into 0 0 times with a remainder of 0.
The number 0 becomes the next digit in our result. 
Result so far: 3723.0625
The remainder is 0 after subtracting 0 from 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 3723.0625, and the remainder is 0.0.