Test for Divisibility of Numbers

Prove the following property of divisibility:

If $a,b,$ and $c$ are three natural numbers such that $a$ is divisible by $b$, and $b$ is divisible by $c$, then $a$ is divisible by $c$ also.

Explain the following property with the help of an example

If $a,b,$ and $c$ are three natural numbers such that $a$ is divisible by $b$, and $b$ is divisible by $c$, then $a$ is divisible by $c$ also.

Explain the following property with the help of an example

If a number is divisible by another number, then it is divisible by each of the factors of that number.

Create two different four-digit numbers that are divisible by: 

$4, 6$ and $9$

The number $50$_____$19$ is exactly divisible by $9$.

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$90990$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$85446$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$35932$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$20704$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$67722$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$9410$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$67713$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$67704$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$99483$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$8289$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$7535$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$225$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$128$

Find whether the given number is divisible by $4$ and $8$.

$25608$

Try whether the given number is divisible by $2, 3, 4, 5, 6, 8, 9$ and $10$.

$333$