61374 ÷ 9 = 6819 R3
Alright, let's work through the division of 61374 by 9 step by step.

Step 1:
9 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 (1) of the dividend behind the 6 and repeat the process: 61 / 9

Step 2:
9 goes into 61 6 times with a remainder of 7.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 54 from 61 to get 7.
Bring next digit (3) of the dividend behind the 7 and repeat the process: 73 / 9

Step 3:
9 goes into 73 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 68
Subtract 72 from 73 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 9

Step 4:
9 goes into 17 1 times with a remainder of 8.
Write down 1 as next digit of of the result. 
Result so far: 681
Subtract 9 from 17 to get 8.
Bring next digit (4) of the dividend behind the 8 and repeat the process: 84 / 9

Step 5:
9 goes into 84 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 6819
Subtract 81 from 84 to get 3.

The final result is 6819 with a remainder of 3.