77244 ÷ 7 = 11034 R6
Alright, let's work through the division of 77244 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 (7) of the dividend behind the 0 and repeat the process: 7 / 7

Step 2:
7 goes into 7 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 7 from 7 to get 0.
Bring next digit (2) of the dividend behind the 0 and repeat the process: 2 / 7

Step 3:
7 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 110
Subtract 0 from 2 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 7

Step 4:
7 goes into 24 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 1103
Subtract 21 from 24 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: 11034
Subtract 28 from 34 to get 6.

The final result is 11034 with a remainder of 6.