37774 ÷ 7 = 5396 R2
Alright, let's work through the division of 37774 by 7 step by step.

Step 1:
7 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 3 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 7

Step 2:
7 goes into 37 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 5
Subtract 35 from 37 to get 2.
Bring next digit (7) of the dividend behind the 2 and repeat the process: 27 / 7

Step 3:
7 goes into 27 3 times with a remainder of 6.
Write down 3 as next digit of of the result. 
Result so far: 53
Subtract 21 from 27 to get 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 7

Step 4:
7 goes into 67 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 539
Subtract 63 from 67 to get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 7

Step 5:
7 goes into 44 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 5396
Subtract 42 from 44 to get 2.

The final result is 5396 with a remainder of 2.