8053 ÷ 6 = 1342 R1
Alright, let's work through the division of 8053 by 6 step by step.

Step 1:
6 goes into 8 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 8 to get 2.
Bring next digit (0) of the dividend behind the 2 and repeat the process: 20 / 6

Step 2:
6 goes into 20 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 18 from 20 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 6

Step 3:
6 goes into 25 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 134
Subtract 24 from 25 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 6

Step 4:
6 goes into 13 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 1342
Subtract 12 from 13 to get 1.

The final result is 1342 with a remainder of 1.