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

four digit number which are divisible by 4 

then last two digit of the number should be divisible by 4 so,

$=\left(2,4\right),\left(3,2\right)\left(5,2\right),\left(3,6\right),\left(1,2\right),\left(1,6\right),\left(5,6\right),\left(7,2\right),\left(7,6\right),\left(6,4\right)$

10 pairs are possible last two digits divisible by 4

remaining two digits can fill with 20 ways

$$\begin{gathered} =20\times 10 \\ =200 \end{gathered}$$