7537 ÷ 7 = 1076 R5
Alright, let's work through the division of 7537 by 7 step by step.

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 (5) of the dividend behind the 0 and repeat the process: 5 / 7

Step 2:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 5 to get 5.
Bring next digit (3) of the dividend behind the 5 and repeat the process: 53 / 7

Step 3:
7 goes into 53 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 107
Subtract 49 from 53 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 7

Step 4:
7 goes into 47 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 1076
Subtract 42 from 47 to get 5.

The final result is 1076 with a remainder of 5.