Question

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

Answer 1

$\left(i\right)$ The Divisibility Rule of $11$ is $\Rightarrow$ The alternative sum of the digits of Number is divisible by $11$
$\left(ii\right)$ for divisible by $7\Rightarrow$ Take the last digit of the number, double it Then subtract the result from the rest of the number If the resulting number is evenly divisible by 7, so is the original number.
Above Rule can be used to check divisibility of $2156$ by $11$ and $7$ as follows
To check $\left(i\right)$ $2-1+5-6=0$ which is divisible by $11(0=11\ast 0)$
Therefore, Number is Divisible by $11$
To check $\left(ii\right)$ $215-(6\ast 2)=215-12=203$ applying the same rule again $20-(3\ast 2)=20-6=14$ which is divisible by $7$
Therefore, Number is Divisible by $7$
Now, Product $=11\ast 7=77\Rightarrow \frac{2156}{77}=28$
Therefore, $2156$ is divisible by $77$ as well.