We're dividing 2538674 by 16 
We're looking to find how many times 16 goes into 2538674.

On to step 1:
2 divided by 16 is 0 with a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 2 after subtracting 0 from 2.
Fetch the next digit (5) from the dividend, attach it to 2 and continue: 25 / 16

Step 2:
When dividing 25 by 16, we get 1 with a remainder of 9.
Put 1 as the next digit of the answer. 
Result so far: 1.0
The remainder is 9 after subtracting 16 from 25.
Include the next digit (3) from the dividend after 9, then repeat: 93 / 16

Advancing to step 3:
16 goes into 93 5 times with a remainder of 13.
The number 5 becomes the next digit in our result. 
Result so far: 15.0
If we subtract 80 from 93, we get 13.
Bring next digit (8) of the dividend behind the 13 and repeat the process: 138 / 16

Advancing to step 4:
138 divided by 16 is 8 with a remainder of 10.
The next digit of our result is 8. 
Result so far: 158.0
The remainder is 10 after subtracting 128 from 138.
Bring next digit (6) of the dividend behind the 10 and repeat the process: 106 / 16

Step 5:
16 goes into 106 6 times with a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 1586.0
Subtracting 96 from 106 leaves us with 10.
Include the next digit (7) from the dividend after 10, then repeat: 107 / 16

Moving on to step 6:
16 can be fit into 107 6 times, resulting in a remainder of 11.
Use 6 as the next digit of our solution. 
Result so far: 15866.0
The remainder is 11 after subtracting 96 from 107.
Fetch the next digit (4) from the dividend, attach it to 11 and continue: 114 / 16

On to step 7:
114 divided by 16 is 7 with a remainder of 2.
The next digit of our result is 7. 
Result so far: 158667.0
Subtract 112 from 114 to get 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 8:
16 goes into 20 1 times with a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 158667.1
If we subtract 16 from 20, we get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 9:
If we divide 40 by 16, we get 2 and a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 158667.12
Subtracting 32 from 40 leaves us 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.

Let's proceed to step 10:
The number 16 fits into 80 5 times, leaving a remainder of 0.
Record the quotient 5 as the next digit in the result. 
Result so far: 158667.125
Deduct 80 from 80 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Going ahead to step 11:
The number 16 fits into 0 0 times, leaving a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 158667.125
Deduct 0 from 0 and we're left with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

On to step 12:
When dividing 0 by 16, we get 0 with a remainder of 0.
The next digit of our result is 0. 
Result so far: 158667.125
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

The final outcome is 158667.125, with a leftover of 0.0.