Some More Divisibility Rules

If $A679B$ is a $5$ digit number is divisible by $72$ find $\text{'}A\text{'}$ and $\text{'}B\text{'}$?

Check whether ${32}^2$ is divisible by $4$ or $8$ or by both $4$ and $8$?

Check whether $2^2+2^3+2^4$ is divisible by $2$ or $4$ or by both $2$ and $4$?

Check whether $876$ and $345$ are divisible by $3$? Also check whether $3$ divides the difference of $876$ and $345$?

Check whether $456$ and $618$ are divisible by $6$? Also, check whether $6$ divides the sum of $456$ and $618$?

Check whether $1435$ is divisible by $5$ and $7$? Verify if $1435$ is divisible by the product of $5$ and $7$?

Check whether $2156$ is divisible by $11$ and $7$? Verify whether $2156$ is a divisible by-product of $11$ and $7$?

Check whether $756$ is divisible by $42$? Verify whether $756$ is divisible by all the factors of $42$?

Check whether $864$ is divisible by $36$? Verify whether $864$ is divisible by all the factors of $36$?

Check whether $61479$ is divisible by $81$.

Check whether $25110$ is divisible by $45$.

Check whether $1576\times 1577\times 1578$ is divisible by $3$ or not.

Check whether $3^3-3^2$ is divisible by $3$? Explain

Check whether $2^3+2^4+2^5$ is divisible by $2$? Explain

$144$ is divisible by $12$. Is it divisible by the factors of $12$? Verify.

Check whether $1008$ is divisible by $6$ or not.

Check whether $456$ is divisible by $6$ or not.

Check whether $1632$ is divisible by $6$ or not.

Check whether $4542$ is divisible by $3$ or $9$ or by both.

Check whether $3789$ is divisible by $3$ or $9$ or by both.