95024 ÷ 7 = 13574 R6
Alright, let's work through the division of 95024 by 7 step by step.

Step 1:
7 goes into 9 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 9 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 7

Step 2:
7 goes into 25 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 13
Subtract 21 from 25 to get 4.
Bring next digit (0) of the dividend behind the 4 and repeat the process: 40 / 7

Step 3:
7 goes into 40 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 135
Subtract 35 from 40 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 7

Step 4:
7 goes into 52 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 1357
Subtract 49 from 52 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 7

Step 5:
7 goes into 34 4 times with a remainder of 6.
Write down 4 as next digit of of the result. 
Result so far: 13574
Subtract 28 from 34 to get 6.

The final result is 13574 with a remainder of 6.