55124 ÷ 4 = 13781 R0
Alright, let's work through the division of 55124 by 4 step by step.

Step 1:
4 goes into 5 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 5 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 4

Step 2:
4 goes into 15 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 12 from 15 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 4

Step 3:
4 goes into 31 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 137
Subtract 28 from 31 to get 3.
Bring next digit (2) of the dividend behind the 3 and repeat the process: 32 / 4

Step 4:
4 goes into 32 8 times with a remainder of 0.
Write down 8 as next digit of of the result. 
Result so far: 1378
Subtract 32 from 32 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 4

Step 5:
4 goes into 4 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 13781
Subtract 4 from 4 to get 0.

The final result is 13781 with a remainder of 0.