42105 ÷ 8 = 5263 R1
Alright, let's work through the division of 42105 by 8 step by step.

Step 1:
8 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (2) of the dividend behind the 4 and repeat the process: 42 / 8

Step 2:
8 goes into 42 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 40 from 42 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 8

Step 3:
8 goes into 21 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 52
Subtract 16 from 21 to get 5.
Bring next digit (0) of the dividend behind the 5 and repeat the process: 50 / 8

Step 4:
8 goes into 50 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 526
Subtract 48 from 50 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 8

Step 5:
8 goes into 25 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 5263
Subtract 24 from 25 to get 1.

The final result is 5263 with a remainder of 1.