15535 ÷ 7 = 2219 R2
Alright, let's work through the division of 15535 by 7 step by step.

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 (5) of the dividend behind the 1 and repeat the process: 15 / 7

Step 2:
7 goes into 15 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 14 from 15 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 7

Step 3:
7 goes into 15 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 22
Subtract 14 from 15 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 7

Step 4:
7 goes into 13 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 221
Subtract 7 from 13 to get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 7

Step 5:
7 goes into 65 9 times with a remainder of 2.
Write down 9 as next digit of of the result. 
Result so far: 2219
Subtract 63 from 65 to get 2.

The final result is 2219 with a remainder of 2.