Are These Numbers Too Big?

$72=9\times8$
So the number a679b should be divisible by 8 and 9.
So, according to divisibility rules of 8,
The last three digits of the number should be divisible by 8.
Thus, $b=2$ .

Now, according to divisibility rules of 9,
The sum of the digits should be divisible by 9..
Thus, $a=3$ .

Therefore, the number is $\boxed{36792}$ .

$72=8\times 9\Rightarrow 4|9b$ there are two posibilities $b=2$ or $6$ , also $8|79b$ , thus $b=2$ . Then, the sum of digits should be divisible by $9\Rightarrow a=3$

$\boxed{36792}$ is the number