53515 ÷ 4 = 13378 R3
Alright, let's work through the division of 53515 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 (3) of the dividend behind the 1 and repeat the process: 13 / 4

Step 2:
4 goes into 13 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 12 from 13 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: 133
Subtract 12 from 15 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 4

Step 4:
4 goes into 31 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 1337
Subtract 28 from 31 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 4

Step 5:
4 goes into 35 8 times with a remainder of 3.
Write down 8 as next digit of of the result. 
Result so far: 13378
Subtract 32 from 35 to get 3.

The final result is 13378 with a remainder of 3.