57639 ÷ 7 = 8234 R1
Alright, let's work through the division of 57639 by 7 step by step.

Step 1:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 7

Step 2:
7 goes into 57 8 times with a remainder of 1.
Write down 8 as next digit of of the result. 
Result so far: 8
Subtract 56 from 57 to get 1.
Bring next digit (6) of the dividend behind the 1 and repeat the process: 16 / 7

Step 3:
7 goes into 16 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 82
Subtract 14 from 16 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 7

Step 4:
7 goes into 23 3 times with a remainder of 2.
Write down 3 as next digit of of the result. 
Result so far: 823
Subtract 21 from 23 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 7

Step 5:
7 goes into 29 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 8234
Subtract 28 from 29 to get 1.

The final result is 8234 with a remainder of 1.