We look at the division of 45377 by 59 
We're looking to find how many times 59 goes into 45377.

Moving on to step 1:
59 goes into 4 0 times with a remainder of 4.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Append the next digit (5) from the dividend to 4 and continue with: 45 / 59

On to step 2:
59 goes into 45 0 times with a remainder of 45.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 45 after subtracting 0 from 45.
Bring next digit (3) of the dividend behind the 45 and repeat the process: 453 / 59

On to step 3:
453 divided by 59 is 7 with a remainder of 40.
Write down 7 as next digit of the result. 
Result so far: 7.0
The remainder is 40 after subtracting 413 from 453.
Bring next digit (7) of the dividend behind the 40 and repeat the process: 407 / 59

Advancing to step 4:
The number 59 fits into 407 6 times, leaving a remainder of 53.
Use 6 as the next digit of our solution. 
Result so far: 76.0
If we take 354 away from 407, we end up with 53.
Include the next digit (7) from the dividend after 53, then repeat: 537 / 59

Advancing to step 5:
The number 59 fits into 537 9 times, leaving a remainder of 6.
Use 9 as the next digit of our solution. 
Result so far: 769.0
Subtract 531 from 537 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 6:
The number 59 fits into 60 1 times, leaving a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 769.1
The remainder is 1 after subtracting 59 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 7:
If we divide 10 by 59, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 769.1
The remainder is 10 after subtracting 0 from 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:
The number 59 fits into 100 1 times, leaving a remainder of 41.
Use 1 as the next digit of our solution. 
Result so far: 769.101
Subtract 59 from 100 to get 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

On to step 9:
When dividing 410 by 59, we get 6 with a remainder of 56.
Use 6 as the next digit of our solution. 
Result so far: 769.1016
The remainder is 56 after subtracting 354 from 410.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Going ahead to step 10:
The number 59 fits into 560 9 times, leaving a remainder of 29.
Put 9 as the next digit of the answer. 
Result so far: 769.10169
The remainder is 29 after subtracting 531 from 560.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Let's proceed to step 11:
The number 59 fits into 290 4 times, leaving a remainder of 54.
The number 4 becomes the next digit in our result. 
Result so far: 769.101694
If we subtract 236 from 290, we get 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Moving on to step 12:
The number 59 fits into 540 9 times, leaving a remainder of 9.
The number 9 becomes the next digit in our result. 
Result so far: 769.1016949
Deduct 531 from 540 and we're left with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 13:
When dividing 90 by 59, we get 1 with a remainder of 31.
Put 1 as the next digit of the answer. 
Result so far: 769.10169491
If we take 59 away from 90, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

The quotient of the division is 769.10169491, and the remainder is 3.1e-08.