137638 divided by 45 
Let's see how many times 45 fits into 137638.

Step 1:
If we divide 1 by 45, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 45

Advancing to step 2:
45 can be fit into 13 0 times, resulting in a remainder of 13.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 13 to get 13.
Take the next digit (7) from the dividend and append it to 13, then repeat: 137 / 45

Moving on to step 3:
45 can be fit into 137 3 times, resulting in a remainder of 2.
The next digit of our result is 3. 
Result so far: 3.0
If we take 135 away from 137, we end up with 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 45

Advancing to step 4:
45 can be fit into 26 0 times, resulting in a remainder of 26.
Put 0 as the next digit of the answer. 
Result so far: 30.0
If we subtract 0 from 26, we get 26.
Append the next digit (3) from the dividend to 26 and continue with: 263 / 45

Let's proceed to step 5:
45 goes into 263 5 times with a remainder of 38.
Record the quotient 5 as the next digit in the result. 
Result so far: 305.0
If we subtract 225 from 263, we get 38.
Bring next digit (8) of the dividend behind the 38 and repeat the process: 388 / 45

On to step 6:
388 divided by 45 is 8 with a remainder of 28.
The number 8 becomes the next digit in our result. 
Result so far: 3058.0
If we subtract 360 from 388, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 7:
280 divided by 45 is 6 with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 3058.6
Deduct 270 from 280 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 8:
100 divided by 45 is 2 with a remainder of 10.
Write down 2 as next digit of the result. 
Result so far: 3058.62
Subtracting 90 from 100 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 9:
100 divided by 45 is 2 with a remainder of 10.
Put 2 as the next digit of the answer. 
Result so far: 3058.622
Subtract 90 from 100 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

The quotient of the division is 3058.622, and the remainder is 0.001.