2601634 ÷ 953 
Our goal is to divide 2601634 by 953.

Moving on to step 1:
953 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 953

Advancing to step 2:
953 can be fit into 26 0 times, resulting in a remainder of 26.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 26, we end up with 26.
Bring next digit (0) of the dividend behind the 26 and repeat the process: 260 / 953

Step 3:
The number 953 fits into 260 0 times, leaving a remainder of 260.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 260, we get 260.
Grab the next digit (1) from the dividend, add it to 260, then carry on: 2601 / 953

On to step 4:
If we divide 2601 by 953, we get 2 and a remainder of 695.
Put 2 as the next digit of the answer. 
Result so far: 2.0
Subtract 1906 from 2601 to get 695.
Fetch the next digit (6) from the dividend, attach it to 695 and continue: 6956 / 953

Going ahead to step 5:
The number 953 fits into 6956 7 times, leaving a remainder of 285.
Put 7 as the next digit of the answer. 
Result so far: 27.0
Deduct 6671 from 6956 and we're left with 285.
Take the next digit (3) from the dividend and append it to 285, then repeat: 2853 / 953

Moving on to step 6:
953 goes into 2853 2 times with a remainder of 947.
The number 2 becomes the next digit in our result. 
Result so far: 272.0
Subtract 1906 from 2853 to get 947.
Fetch the next digit (4) from the dividend, attach it to 947 and continue: 9474 / 953

Step 7:
If we divide 9474 by 953, we get 9 and a remainder of 897.
Put 9 as the next digit of the answer. 
Result so far: 2729.0
If we take 8577 away from 9474, we end up with 897.
Since there are no more digits in the dividend, we add a zero to the remainder making it 8970, and continue the process.

On to step 8:
The number 953 fits into 8970 9 times, leaving a remainder of 393.
Put 9 as the next digit of the answer. 
Result so far: 2729.9
Subtract 8577 from 8970 to get 393.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3930, and continue the process.

Advancing to step 9:
The number 953 fits into 3930 4 times, leaving a remainder of 118.
Put 4 as the next digit of the answer. 
Result so far: 2729.94
If we take 3812 away from 3930, we end up with 118.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1180, and continue the process.

On to step 10:
953 can be fit into 1180 1 times, resulting in a remainder of 227.
Put 1 as the next digit of the answer. 
Result so far: 2729.941
If we subtract 953 from 1180, we get 227.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2270, and continue the process.

Moving on to step 11:
953 can be fit into 2270 2 times, resulting in a remainder of 364.
The next digit of our result is 2. 
Result so far: 2729.9412
Subtracting 1906 from 2270 leaves us with 364.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3640, and continue the process.

Moving on to step 12:
If we divide 3640 by 953, we get 3 and a remainder of 781.
Put 3 as the next digit of the answer. 
Result so far: 2729.94123
Subtracting 2859 from 3640 leaves us with 781.
Since there are no more digits in the dividend, we add a zero to the remainder making it 7810, and continue the process.

Step 13:
953 can be fit into 7810 8 times, resulting in a remainder of 186.
Use 8 as the next digit of our solution. 
Result so far: 2729.941238
If we subtract 7624 from 7810, we get 186.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1860, and continue the process.

Going ahead to step 14:
1860 divided by 953 is 1 with a remainder of 907.
Write down 1 as next digit of the result. 
Result so far: 2729.9412381
If we subtract 953 from 1860, we get 907.
Since there are no more digits in the dividend, we add a zero to the remainder making it 9070, and continue the process.

Moving on to step 15:
When dividing 9070 by 953, we get 9 with a remainder of 493.
The next digit of our result is 9. 
Result so far: 2729.94123819
If we subtract 8577 from 9070, we get 493.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4930, and continue the process.

The quotient of the division is 2729.94123819, and the remainder is 4.93e-07.