44619 ÷ 6 = 7436 R3
Alright, let's work through the division of 44619 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 (6) of the dividend behind the 2 and repeat the process: 26 / 6

Step 3:
6 goes into 26 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 74
Subtract 24 from 26 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 6

Step 4:
6 goes into 21 3 times with a remainder of 3.
Write down 3 as next digit of of the result. 
Result so far: 743
Subtract 18 from 21 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 6

Step 5:
6 goes into 39 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 7436
Subtract 36 from 39 to get 3.

The final result is 7436 with a remainder of 3.