71978 ÷ 7 = 10282 R4
Alright, let's work through the division of 71978 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 (1) of the dividend behind the 0 and repeat the process: 1 / 7

Step 2:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 7

Step 3:
7 goes into 19 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 102
Subtract 14 from 19 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: 1028
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: 10282
Subtract 14 from 18 to get 4.

The final result is 10282 with a remainder of 4.