45943 ÷ 4 = 11485 R3
Alright, let's work through the division of 45943 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 (5) of the dividend behind the 0 and repeat the process: 5 / 4

Step 2:
4 goes into 5 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 11
Subtract 4 from 5 to get 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 4

Step 3:
4 goes into 19 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 114
Subtract 16 from 19 to get 3.
Bring next digit (4) of the dividend behind the 3 and repeat the process: 34 / 4

Step 4:
4 goes into 34 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 1148
Subtract 32 from 34 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 4

Step 5:
4 goes into 23 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 11485
Subtract 20 from 23 to get 3.

The final result is 11485 with a remainder of 3.