434668 ÷ 61 
We're looking to find how many times 61 goes into 434668.

Let's proceed to step 1:
61 can be fit into 4 0 times, resulting in a remainder of 4.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 4, we get 4.
Take the next digit (3) from the dividend and append it to 4, then repeat: 43 / 61

On to step 2:
When dividing 43 by 61, we get 0 with a remainder of 43.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we take 0 away from 43, we end up with 43.
Grab the next digit (4) from the dividend, add it to 43, then carry on: 434 / 61

Going ahead to step 3:
If we divide 434 by 61, we get 7 and a remainder of 7.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we take 427 away from 434, we end up with 7.
Fetch the next digit (6) from the dividend, attach it to 7 and continue: 76 / 61

Step 4:
If we divide 76 by 61, we get 1 and a remainder of 15.
Use 1 as the next digit of our solution. 
Result so far: 71.0
Subtract 61 from 76 to get 15.
Include the next digit (6) from the dividend after 15, then repeat: 156 / 61

Let's proceed to step 5:
61 goes into 156 2 times with a remainder of 34.
The number 2 becomes the next digit in our result. 
Result so far: 712.0
Subtracting 122 from 156 leaves us with 34.
Include the next digit (8) from the dividend after 34, then repeat: 348 / 61

Let's proceed to step 6:
The number 61 fits into 348 5 times, leaving a remainder of 43.
Use 5 as the next digit of our solution. 
Result so far: 7125.0
If we subtract 305 from 348, we get 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

On to step 7:
61 can be fit into 430 7 times, resulting in a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 7125.7
Subtracting 427 from 430 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.

Step 8:
61 goes into 30 0 times with a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 7125.7
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.

Moving on to step 9:
61 can be fit into 300 4 times, resulting in a remainder of 56.
Write down 4 as next digit of the result. 
Result so far: 7125.704
Subtract 244 from 300 to get 56.
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:
When dividing 560 by 61, we get 9 with a remainder of 11.
The number 9 becomes the next digit in our result. 
Result so far: 7125.7049
The remainder is 11 after subtracting 549 from 560.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 11:
The number 61 fits into 110 1 times, leaving a remainder of 49.
The number 1 becomes the next digit in our result. 
Result so far: 7125.70491
If we subtract 61 from 110, we get 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Going ahead to step 12:
61 goes into 490 8 times with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 7125.704918
If we take 488 away from 490, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 13:
61 can be fit into 20 0 times, resulting in a remainder of 20.
The next digit of our result is 0. 
Result so far: 7125.704918
Subtract 0 from 20 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 14:
If we divide 200 by 61, we get 3 and a remainder of 17.
The number 3 becomes the next digit in our result. 
Result so far: 7125.70491803
If we take 183 away from 200, we end up with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

After the division, we end up with 7125.70491803 and a remainder of 1.7e-08.