66378 ÷ 7 = 9482 R4
Alright, let's work through the division of 66378 by 7 step by step.

Step 1:
7 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 7

Step 2:
7 goes into 66 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 63 from 66 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 7

Step 3:
7 goes into 33 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 94
Subtract 28 from 33 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: 948
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: 9482
Subtract 14 from 18 to get 4.

The final result is 9482 with a remainder of 4.