77503 ÷ 4 = 19375 R3
Alright, let's work through the division of 77503 by 4 step by step.

Step 1:
4 goes into 7 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 7 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 4

Step 2:
4 goes into 37 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 36 from 37 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 4

Step 3:
4 goes into 15 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 193
Subtract 12 from 15 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 4

Step 4:
4 goes into 30 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 1937
Subtract 28 from 30 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 4

Step 5:
4 goes into 23 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 19375
Subtract 20 from 23 to get 3.

The final result is 19375 with a remainder of 3.