13374 ÷ 7 = 1910 R4
Alright, let's work through the division of 13374 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 (3) of the dividend behind the 1 and repeat the process: 13 / 7

Step 2:
7 goes into 13 1 times with a remainder of 6.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 7 from 13 to get 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 7

Step 3:
7 goes into 63 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 63 from 63 to get 0.
Bring next digit (7) of the dividend behind the 0 and repeat the process: 7 / 7

Step 4:
7 goes into 7 1 times with a remainder of 0.
Write down 1 as next digit of of the result. 
Result so far: 191
Subtract 7 from 7 to get 0.
Bring next digit (4) of the dividend behind the 0 and repeat the process: 4 / 7

Step 5:
7 goes into 4 0 times with a remainder of 4.
Write down 0 as next digit of of the result. 
Result so far: 1910
Subtract 0 from 4 to get 4.

The final result is 1910 with a remainder of 4.