61037 ÷ 6 = 10172 R5
Let's divide 61037 by 6.

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

Step 2:
6 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 6

Step 3:
6 goes into 10 1 times with a remainder of 4.
Write down 1 as next digit of of the result. 
Result so far: 101
Subtract 6 from 10 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 6

Step 4:
6 goes into 43 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 1017
Subtract 42 from 43 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: 10172
Subtract 12 from 17 to get 5.

The final result is 10172 with a remainder of 5.