Numbers are to be formed between $1000$ and $3000$, which are divisible by $4$, using the digits $1,2,3,4,5$ and $6$ without repetition of digits. Then the total number of such numbers is _______.

To find total numbers between $1000$ and $3000$ divisible by $4$ using the digits $1,2,3,4,5,6$,

We will solve in two cases.

Case I : When first digit is $1$.

Then last two digits can be $24,32,36,52,56$ or $64$

So, total ways of choosing last two digit is $6$ and second digit will be chosen in $3$ ways

So, number of such numbers $=6\times 3=18$

Case II: When first digit is $2$

Then last two digits can be $16,36,56$ or $64$

So, total ways of choosing last two digit is $4$ and second digit will be chosen in $3$ 

So, number of such numbers $=4\times 3=12$

Total numbers of numbers $=18+12=30$