Divisibility Tests

What is divisibility?

If the eight-digit number $2575d568$ is divisible by $54$ and $87$, the value of the digit '$d$' is

It wouldn't really amaze anybody if you said that $15$ is divisibility by $3$, but what about larger numbers? Use what you learned about divisibility in the student book to identify which of the given number is divisible by the number highlighted.

$\mathbf{8}\to 12046, 23184, 48714, 38196$

Use your knowledge of the divisibility chart to help you decide if these numbers are prime or composite. The first answer has been circled for you.

A number divisible by $8$ can never end with

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

Choose the number that is divisible by $8$.

Choose the number that is divisible by $8$.

Test the divisibility of the following numbers by $10$.

Find the number that is not divisible by $10$

Find the number that is divisible by $100$.

If a number is exactly divisible by both $3$ and $4$, then the number is divisible by: 

If the $9$-digit number $89\mathrm{x}64287\mathrm{y}$is divisible by $72$, then what is the value of $(3\mathrm{x} + 2\mathrm{y})$?

If a nine-digit number $7698x138y$ is divisible by $72$. then the value of $\sqrt{4x+y}$ is______.

If an eleven-digit number $6578x43267y$ is divisible by $72$, then the value of $\sqrt{x+6y}$ will be _____.

If th nine digit number $48c4923y8$ is divisible by $88$, then the value of $\left(6x+5y\right)$ for the maximum value of $y$, will be _____.

If a nine-digit number $489x6378y$ is divisible by $72$, then the value of $\sqrt{8x+6y}$ will be:

Numbers that have more than two factors are called composite factors.

Which numbers from the below are exactly divisible by $2, 3, 4, 6$ and $9$ ?

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.