We look at the division of 353669 by 46 
We want to figure out the number of times 353669 can be divided by 46.

Going ahead to step 1:
If we divide 3 by 46, we get 0 and a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Take the next digit (5) from the dividend and append it to 3, then repeat: 35 / 46

Let's proceed to step 2:
46 goes into 35 0 times with a remainder of 35.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 35 after subtracting 0 from 35.
Bring next digit (3) of the dividend behind the 35 and repeat the process: 353 / 46

Going ahead to step 3:
The number 46 fits into 353 7 times, leaving a remainder of 31.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Subtract 322 from 353 to get 31.
Fetch the next digit (6) from the dividend, attach it to 31 and continue: 316 / 46

Step 4:
The number 46 fits into 316 6 times, leaving a remainder of 40.
Record the quotient 6 as the next digit in the result. 
Result so far: 76.0
Subtract 276 from 316 to get 40.
Append the next digit (6) from the dividend to 40 and continue with: 406 / 46

Going ahead to step 5:
46 can be fit into 406 8 times, resulting in a remainder of 38.
Use 8 as the next digit of our solution. 
Result so far: 768.0
The remainder is 38 after subtracting 368 from 406.
Append the next digit (9) from the dividend to 38 and continue with: 389 / 46

Advancing to step 6:
389 divided by 46 is 8 with a remainder of 21.
Record the quotient 8 as the next digit in the result. 
Result so far: 7688.0
If we subtract 368 from 389, we get 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

On to step 7:
46 can be fit into 210 4 times, resulting in a remainder of 26.
Use 4 as the next digit of our solution. 
Result so far: 7688.4
Subtract 184 from 210 to get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Going ahead to step 8:
If we divide 260 by 46, we get 5 and a remainder of 30.
Record the quotient 5 as the next digit in the result. 
Result so far: 7688.45
Subtract 230 from 260 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 9:
300 divided by 46 is 6 with a remainder of 24.
The number 6 becomes the next digit in our result. 
Result so far: 7688.456
Subtracting 276 from 300 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 10:
When dividing 240 by 46, we get 5 with a remainder of 10.
Put 5 as the next digit of the answer. 
Result so far: 7688.4565
The remainder is 10 after subtracting 230 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 11:
When dividing 100 by 46, we get 2 with a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 7688.45652
If we take 92 away from 100, we end up with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Going ahead to step 12:
The number 46 fits into 80 1 times, leaving a remainder of 34.
Record the quotient 1 as the next digit in the result. 
Result so far: 7688.456521
Deduct 46 from 80 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Advancing to step 13:
The number 46 fits into 340 7 times, leaving a remainder of 18.
The number 7 becomes the next digit in our result. 
Result so far: 7688.4565217
Deduct 322 from 340 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Let's proceed to step 14:
180 divided by 46 is 3 with a remainder of 42.
Use 3 as the next digit of our solution. 
Result so far: 7688.45652173
The remainder is 42 after subtracting 138 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

The final result is 7688.45652173 with a remainder of 4.2e-08.