6523 ÷ 4 = 1630 R3
Alright, let's work through the division of 6523 by 4 step by step.

Step 1:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 6 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 4

Step 2:
4 goes into 25 6 times with a remainder of 1.
Write down 6 as next digit of of the result. 
Result so far: 16
Subtract 24 from 25 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 4

Step 3:
4 goes into 12 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 163
Subtract 12 from 12 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 4

Step 4:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 1630
Subtract 0 from 3 to get 3.

The final result is 1630 with a remainder of 3.