Tests of Divisibility

Prove by expanding $730$ is divisible by $10$.

Prove the divisibility rule of $3$.

Prove the divisibility rule of $2$.

Prove the divisibility rule of $5$.

The number $995$ is divisible by $10$.

Check whether $10005$ divisible by $10$ or not without actually dividing.

Find out if the following number is divisible by 11 or not.

$4543$

Check whether a number $119$ is divisible by $7.$

Is $905$ divisible by $7$?

If $2\mathrm{x}248$ is a multiple of $11$, where $\mathrm{x}$ is a digit, what is value of $\mathrm{x}$?

If $86\mathrm{x}6194$ is a multiple of $11$, where $\mathrm{x}$ is a digit, what is value of $\mathrm{x}$?

If $64\mathrm{x}2456$ is a multiple of $11$, where $\mathrm{x}$ is a digit, what is value of $\mathrm{x}$?

If $32\mathrm{z}6$ is a multiple of $3$, where $\mathrm{z}$ is a digit, what is value of $\mathrm{z}$?

If $42\mathrm{z}3$ is a multiple of $9$, where $\mathrm{z}$ is a digit, what is value of $\mathrm{z}$?

If $\frac{696}{2}=x$, find the value of $x$.

Show that if $d_1\mid a$ and $d_2\mid d_1, d_1>0, d_2>0$ then $d_2\mid a$.

If a number $N$ divided by $2$ leaves no remainder, the sum of all possible values of the digit in the ones place is _____.

If $abc$ is a $3-$digit number, then find the largest one-digit number that divides $\left(abc-a-b-c\right)$ exactly.

If $56b$ is a multiple of $9$, then what could be the possible value of $b$?

If the division $N÷5$ leaves a remainder of $3$ and the division $N÷2$ leaves no remainder, then what could be the possible value of digit at ones place?