42257 ÷ 4 = 10564 R1
No problem, we've got 42257 and 4 for the division.

Step 1:
4 goes into 4 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 4 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 4

Step 2:
4 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 2 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 4

Step 3:
4 goes into 22 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 105
Subtract 20 from 22 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 4

Step 4:
4 goes into 25 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 1056
Subtract 24 from 25 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 4

Step 5:
4 goes into 17 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 10564
Subtract 16 from 17 to get 1.

The final result is 10564 with a remainder of 1.