52338 ÷ 4 = 13084 R2
Alright, let's work through the division of 52338 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 (2) of the dividend behind the 1 and repeat the process: 12 / 4

Step 2:
4 goes into 12 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 12 from 12 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 4

Step 3:
4 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 130
Subtract 0 from 3 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 4

Step 4:
4 goes into 33 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 1308
Subtract 32 from 33 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 4

Step 5:
4 goes into 18 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 13084
Subtract 16 from 18 to get 2.

The final result is 13084 with a remainder of 2.