21137 ÷ 7 = 3019 R4
Alright, let's work through the division of 21137 by 7 step by step.

Step 1:
7 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 7

Step 2:
7 goes into 21 3 times with a remainder of 0.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 21 from 21 to get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 7

Step 3:
7 goes into 1 0 times with a remainder of 1.
Write down 0 as next digit of of the result. 
Result so far: 30
Subtract 0 from 1 to get 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 7

Step 4:
7 goes into 13 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 301
Subtract 7 from 13 to get 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 7

Step 5:
7 goes into 67 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 3019
Subtract 63 from 67 to get 4.

The final result is 3019 with a remainder of 4.