15872 ÷ 7 = 2267 R3
Alright, let's work through the division of 15872 by 7 step by step.

Step 1:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 1 to get 1.
Bring next digit (5) of the dividend behind the 1 and repeat the process: 15 / 7

Step 2:
7 goes into 15 2 times with a remainder of 1.
Write down 2 as next digit of of the result. 
Result so far: 2
Subtract 14 from 15 to get 1.
Bring next digit (8) of the dividend behind the 1 and repeat the process: 18 / 7

Step 3:
7 goes into 18 2 times with a remainder of 4.
Write down 2 as next digit of of the result. 
Result so far: 22
Subtract 14 from 18 to get 4.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 7

Step 4:
7 goes into 47 6 times with a remainder of 5.
Write down 6 as next digit of of the result. 
Result so far: 226
Subtract 42 from 47 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 7

Step 5:
7 goes into 52 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 2267
Subtract 49 from 52 to get 3.

The final result is 2267 with a remainder of 3.