Question

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

Answer 1

First we have to break $42$ into factors $7$ and $6$ and
Now, we have to check simultaneously both the conditions of divisibility by $7$ and $6$
$\left(i\right)$ for divisible by $7$, To check if a number is evenly divisible by 7: 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.
$\left(ii\right)$ for divisible by $6$, it must also be divisible by 2 and 3. Therefore, we need to check if a number is even and then check if the sum of the digits is divisible by 3.
To check $\left(i\right)$ $756-(6\ast 2)=75-12=63$ which is divisible by $7$
Now, checking for $\left(ii\right)$ it is an even number and $7+5+6=18$ which is divisible by $3$
Therefore $756$ is divisible by $42$.
Now, factors of $42$ are $7,2,3$
Since we have already checked Divisibility of $756$ by $7,2,3$
Hence , $756$ is divisible by all factors of $42$