45813 ÷ 7 = 6544 R5
Alright, let's work through the division of 45813 by 7 step by step.

Step 1:
7 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 4 to get 4.
Bring next digit (5) of the dividend behind the 4 and repeat the process: 45 / 7

Step 2:
7 goes into 45 6 times with a remainder of 3.
Write down 6 as next digit of of the result. 
Result so far: 6
Subtract 42 from 45 to get 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 7

Step 3:
7 goes into 38 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 65
Subtract 35 from 38 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 7

Step 4:
7 goes into 31 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 654
Subtract 28 from 31 to get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 7

Step 5:
7 goes into 33 4 times with a remainder of 5.
Write down 4 as next digit of of the result. 
Result so far: 6544
Subtract 28 from 33 to get 5.

The final result is 6544 with a remainder of 5.