35737 ÷ 3 = 11912 R1
Alright, let's work through the division of 35737 by 3 step by step.

Step 1:
3 goes into 3 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 3 from 3 to get 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 3

Step 2:
3 goes into 5 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 3 from 5 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 3

Step 3:
3 goes into 27 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 119
Subtract 27 from 27 to get 0.
Bring next digit (3) of the dividend behind the 0 and repeat the process: 3 / 3

Step 4:
3 goes into 3 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1191
Subtract 3 from 3 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 3

Step 5:
3 goes into 7 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 11912
Subtract 6 from 7 to get 1.

The final result is 11912 with a remainder of 1.