10677 ÷ 7 = 1525 R2
No problem, we've got 10677 and 7 for the division.

Step 1:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 7

Step 2:
7 goes into 10 1 times with a remainder of 3.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 10 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 7

Step 3:
7 goes into 36 5 times with a remainder of 1.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 35 from 36 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 7

Step 4:
7 goes into 17 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 152
Subtract 14 from 17 to get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 7

Step 5:
7 goes into 37 5 times with a remainder of 2.
Write down 5 as next digit of of the result. 
Result so far: 1525
Subtract 35 from 37 to get 2.

The final result is 1525 with a remainder of 2.