7557 ÷ 6 = 1259 R3
We're going to perform division on 7557 with 6 as the divisor.

Step 1:
6 goes into 7 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 6 from 7 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 6

Step 2:
6 goes into 15 2 times with a remainder of 3.
Write down 2 as next digit of of the result. 
Result so far: 12
Subtract 12 from 15 to get 3.
Bring next digit (5) of the dividend behind the 3 and repeat the process: 35 / 6

Step 3:
6 goes into 35 5 times with a remainder of 5.
Write down 5 as next digit of of the result. 
Result so far: 125
Subtract 30 from 35 to get 5.
Bring next digit (7) of the dividend behind the 5 and repeat the process: 57 / 6

Step 4:
6 goes into 57 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 1259
Subtract 54 from 57 to get 3.

The final result is 1259 with a remainder of 3.