75586065 ÷ 137 
Our goal is to divide 75586065 by 137.

Advancing to step 1:
When dividing 7 by 137, we get 0 with a remainder of 7.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 7 and we're left with 7.
Bring next digit (5) of the dividend behind the 7 and repeat the process: 75 / 137

Let's proceed to step 2:
The number 137 fits into 75 0 times, leaving a remainder of 75.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 75 to get 75.
Fetch the next digit (5) from the dividend, attach it to 75 and continue: 755 / 137

Step 3:
137 can be fit into 755 5 times, resulting in a remainder of 70.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
If we subtract 685 from 755, we get 70.
Include the next digit (8) from the dividend after 70, then repeat: 708 / 137

On to step 4:
137 goes into 708 5 times with a remainder of 23.
The number 5 becomes the next digit in our result. 
Result so far: 55.0
If we take 685 away from 708, we end up with 23.
Take the next digit (6) from the dividend and append it to 23, then repeat: 236 / 137

Moving on to step 5:
If we divide 236 by 137, we get 1 and a remainder of 99.
The number 1 becomes the next digit in our result. 
Result so far: 551.0
If we take 137 away from 236, we end up with 99.
Bring next digit (0) of the dividend behind the 99 and repeat the process: 990 / 137

Step 6:
When dividing 990 by 137, we get 7 with a remainder of 31.
The number 7 becomes the next digit in our result. 
Result so far: 5517.0
Subtract 959 from 990 to get 31.
Bring next digit (6) of the dividend behind the 31 and repeat the process: 316 / 137

Let's proceed to step 7:
137 goes into 316 2 times with a remainder of 42.
Put 2 as the next digit of the answer. 
Result so far: 55172.0
Deduct 274 from 316 and we're left with 42.
Bring next digit (5) of the dividend behind the 42 and repeat the process: 425 / 137

On to step 8:
137 can be fit into 425 3 times, resulting in a remainder of 14.
The next digit of our result is 3. 
Result so far: 551723.0
The remainder is 14 after subtracting 411 from 425.
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 9:
When dividing 140 by 137, we get 1 with a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 551723.1
Subtracting 137 from 140 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

On to step 10:
137 can be fit into 30 0 times, resulting in a remainder of 30.
Use 0 as the next digit of our solution. 
Result so far: 551723.1
The remainder is 30 after subtracting 0 from 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 11:
137 goes into 300 2 times with a remainder of 26.
Record the quotient 2 as the next digit in the result. 
Result so far: 551723.102
The remainder is 26 after subtracting 274 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Step 12:
If we divide 260 by 137, we get 1 and a remainder of 123.
Write down 1 as next digit of the result. 
Result so far: 551723.1021
Deduct 137 from 260 and we're left with 123.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1230, and continue the process.

On to step 13:
1230 divided by 137 is 8 with a remainder of 134.
The number 8 becomes the next digit in our result. 
Result so far: 551723.10218
Deduct 1096 from 1230 and we're left with 134.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1340, and continue the process.

Advancing to step 14:
The number 137 fits into 1340 9 times, leaving a remainder of 107.
The next digit of our result is 9. 
Result so far: 551723.102189
Deduct 1233 from 1340 and we're left with 107.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1070, and continue the process.

Advancing to step 15:
The number 137 fits into 1070 7 times, leaving a remainder of 111.
The next digit of our result is 7. 
Result so far: 551723.1021897
The remainder is 111 after subtracting 959 from 1070.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1110, and continue the process.

Moving on to step 16:
If we divide 1110 by 137, we get 8 and a remainder of 14.
Put 8 as the next digit of the answer. 
Result so far: 551723.10218978
If we take 1096 away from 1110, we end up 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.

The quotient of the division is 551723.10218978, and the remainder is 1.4e-08.