2953 ÷ 7 = 421 R6
Alright, let's work through the division of 2953 by 7 step by step.

Step 1:
7 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 7

Step 2:
7 goes into 29 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 28 from 29 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: 42
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: 421
Subtract 7 from 13 to get 6.

The final result is 421 with a remainder of 6.