44117 ÷ 6 = 7352 R5
Alright, let's work through the division of 44117 by 6 step by step.

Step 1:
6 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 6

Step 2:
6 goes into 44 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 42 from 44 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 3:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 73
Subtract 18 from 21 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 6

Step 4:
6 goes into 31 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 735
Subtract 30 from 31 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 6

Step 5:
6 goes into 17 2 times with a remainder of 5.
Write down 2 as next digit of of the result. 
Result so far: 7352
Subtract 12 from 17 to get 5.

The final result is 7352 with a remainder of 5.