6349 ÷ 4 = 1587 R1
Alright, let's work through the division of 6349 by 4 step by step.

Step 1:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 6 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 4

Step 2:
4 goes into 23 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 20 from 23 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 4

Step 3:
4 goes into 34 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 158
Subtract 32 from 34 to get 2.
Bring next digit (9) of the dividend behind the 2 and repeat the process: 29 / 4

Step 4:
4 goes into 29 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 1587
Subtract 28 from 29 to get 1.

The final result is 1587 with a remainder of 1.