37639 ÷ 7 = 5377 R0
Alright, let's work through the division of 37639 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 (6) of the dividend behind the 2 and repeat the process: 26 / 7

Step 3:
7 goes into 26 3 times with a remainder of 5.
Write down 3 as next digit of of the result. 
Result so far: 53
Subtract 21 from 26 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 7

Step 4:
7 goes into 53 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 537
Subtract 49 from 53 to get 4.
Bring next digit (9) of the dividend behind the 4 and repeat the process: 49 / 7

Step 5:
7 goes into 49 7 times with a remainder of 0.
Write down 7 as next digit of of the result. 
Result so far: 5377
Subtract 49 from 49 to get 0.

The final result is 5377 with a remainder of 0.