35578 ÷ 7 = 5082 R4
Alright, let's work through the division of 35578 by 7 step by step.

Step 1:
7 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 7

Step 2:
7 goes into 35 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 35 from 35 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 7

Step 3:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 50
Subtract 0 from 5 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 7

Step 4:
7 goes into 57 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 508
Subtract 56 from 57 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 7

Step 5:
7 goes into 18 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 5082
Subtract 14 from 18 to get 4.

The final result is 5082 with a remainder of 4.