41378 ÷ 4 = 10344 R2
Alright, let's work through the division of 41378 by 4 step by step.

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

Step 2:
4 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 10
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 4

Step 3:
4 goes into 13 3 times with a remainder of 1.
Write down 3 as next digit of of the result. 
Result so far: 103
Subtract 12 from 13 to get 1.
Bring next digit (7) of the dividend behind the 1 and repeat the process: 17 / 4

Step 4:
4 goes into 17 4 times with a remainder of 1.
Write down 4 as next digit of of the result. 
Result so far: 1034
Subtract 16 from 17 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 4

Step 5:
4 goes into 18 4 times with a remainder of 2.
Write down 4 as next digit of of the result. 
Result so far: 10344
Subtract 16 from 18 to get 2.

The final result is 10344 with a remainder of 2.