The number of four digit numbers that can be formed using the digits $1,2,3,4,5,6,7$ which are divisible by 4 , when the repetition of any digit is not allowed, is

$1,2,3,4,5,6,7$ For number of numbers divisible by 4 , unit digit can be either of $2,4,6$. When unit digit is 2 , digit at tens place can be $1,3,5,7$. $\therefore \quad$ Possible numbers $\frac{}{4} \times \frac{}{5} \times \frac{}{4} \times \frac{2}{1}=80$ When unit digit is 4 , digits at tens place can be 2,6 . $\therefore \quad$ Possible numbers $\frac{}{4} \times \frac{}{5} \times \frac{}{2} \times \frac{4}{1}=40$ When unit digit is 6 , digit at tens place can be $1,3,5,7$. $\therefore \quad$ Possible numbers $\frac{}{4} \times \frac{}{5} \times \frac{}{4} \times \frac{6}{1}=80$ $\therefore \quad$ Total number of numbers $=80+40+80=200$.