31003 ÷ 4 = 7750 R3
Alright, let's work through the division of 31003 by 4 step by step.

Step 1:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 4

Step 2:
4 goes into 31 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 28 from 31 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 4

Step 3:
4 goes into 30 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 77
Subtract 28 from 30 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 4

Step 4:
4 goes into 20 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 775
Subtract 20 from 20 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 4

Step 5:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 7750
Subtract 0 from 3 to get 3.

The final result is 7750 with a remainder of 3.