7669 ÷ 7 = 1095 R4
Let's divide 7669 by 7.

Step 1:
7 goes into 7 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 7 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 7

Step 2:
7 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 6 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 7

Step 3:
7 goes into 66 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 109
Subtract 63 from 66 to get 3.
Bring next digit (9) of the dividend behind the 3 and repeat the process: 39 / 7

Step 4:
7 goes into 39 5 times with a remainder of 4.
Write down 5 as next digit of of the result. 
Result so far: 1095
Subtract 35 from 39 to get 4.

The final result is 1095 with a remainder of 4.