6421 ÷ 7 = 917 R2
We're going to perform division on 6421 with 7 as the divisor.

Step 1:
7 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 6 to get 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 7

Step 2:
7 goes into 64 9 times with a remainder of 1.
Write down 9 as next digit of of the result. 
Result so far: 9
Subtract 63 from 64 to get 1.
Bring next digit (2) of the dividend behind the 1 and repeat the process: 12 / 7

Step 3:
7 goes into 12 1 times with a remainder of 5.
Write down 1 as next digit of of the result. 
Result so far: 91
Subtract 7 from 12 to get 5.
Bring next digit (1) of the dividend behind the 5 and repeat the process: 51 / 7

Step 4:
7 goes into 51 7 times with a remainder of 2.
Write down 7 as next digit of of the result. 
Result so far: 917
Subtract 49 from 51 to get 2.

The final result is 917 with a remainder of 2.