13764 ÷ 7 = 1966 R2
Alright, let's work through the division of 13764 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 (7) of the dividend behind the 6 and repeat the process: 67 / 7

Step 3:
7 goes into 67 9 times with a remainder of 4.
Write down 9 as next digit of of the result. 
Result so far: 19
Subtract 63 from 67 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 7

Step 4:
7 goes into 46 6 times with a remainder of 4.
Write down 6 as next digit of of the result. 
Result so far: 196
Subtract 42 from 46 to get 4.
Bring next digit (4) of the dividend behind the 4 and repeat the process: 44 / 7

Step 5:
7 goes into 44 6 times with a remainder of 2.
Write down 6 as next digit of of the result. 
Result so far: 1966
Subtract 42 from 44 to get 2.

The final result is 1966 with a remainder of 2.