75127 ÷ 7 = 10732 R3
Alright, let's work through the division of 75127 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 (1) of the dividend behind the 5 and repeat the process: 51 / 7

Step 3:
7 goes into 51 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 107
Subtract 49 from 51 to get 2.
Bring next digit (2) of the dividend behind the 2 and repeat the process: 22 / 7

Step 4:
7 goes into 22 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 1073
Subtract 21 from 22 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 7

Step 5:
7 goes into 17 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 10732
Subtract 14 from 17 to get 3.

The final result is 10732 with a remainder of 3.