61738 ÷ 7 = 8819 R5
Alright, let's work through the division of 61738 by 7 step by step.

Step 1:
7 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 / 7

Step 2:
7 goes into 61 8 times with a remainder of 5.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 56 from 61 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 7

Step 3:
7 goes into 57 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 88
Subtract 56 from 57 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 7

Step 4:
7 goes into 13 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 881
Subtract 7 from 13 to get 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 7

Step 5:
7 goes into 68 9 times with a remainder of 5.
Write down 9 as next digit of of the result. 
Result so far: 8819
Subtract 63 from 68 to get 5.

The final result is 8819 with a remainder of 5.