45864 ÷ 3 = 15288 R0
Alright, let's work through the division of 45864 by 3 step by step.

Step 1:
3 goes into 4 1 times with a remainder of 1.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 3 from 4 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 3

Step 2:
3 goes into 15 5 times with a remainder of 0.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 15 from 15 to get 0.
Bring next digit (8) of the dividend behind the 0 and repeat the process: 8 / 3

Step 3:
3 goes into 8 2 times with a remainder of 2.
Write down 2 as next digit of of the result. 
Result so far: 152
Subtract 6 from 8 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 3

Step 4:
3 goes into 26 8 times with a remainder of 2.
Write down 8 as next digit of of the result. 
Result so far: 1528
Subtract 24 from 26 to get 2.
Bring next digit (4) of the dividend behind the 2 and repeat the process: 24 / 3

Step 5:
3 goes into 24 8 times with a remainder of 0.
Write down 8 as next digit of of the result. 
Result so far: 15288
Subtract 24 from 24 to get 0.

The final result is 15288 with a remainder of 0.