75842 ÷ 7 = 10834 R4
Alright, let's work through the division of 75842 by 7 step by step.

Step 1:
7 goes into 7 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 7 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 7

Step 2:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 5 to get 5.
Bring next digit (8) of the dividend behind the 5 and repeat the process: 58 / 7

Step 3:
7 goes into 58 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 108
Subtract 56 from 58 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 7

Step 4:
7 goes into 24 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 1083
Subtract 21 from 24 to get 3.
Bring next digit (2) of the dividend behind the 3 and repeat the process: 32 / 7

Step 5:
7 goes into 32 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 10834
Subtract 28 from 32 to get 4.

The final result is 10834 with a remainder of 4.