Division

Prime number - a natural number that is divisible only by itself and $1$.
For example: the number $11$.
We can divide $11$ without a remainder only by $11$ or by $1$, which makes it a prime number.

Composite number - a number that can be expressed as a product of two natural numbers smaller than itself, which are not $1$ and the number itself.
Every even number is also a composite number, except for the number $2$.
For example:
The number $16$. We can divide $16$ by $2$ without a remainder, or by $8$ or by $4$. This makes it a composite number because it can be divided by numbers other than itself and $1$.

The number $1$ - a special number that is neither prime nor composite.
The number $2$ - the only even prime number.

Click here to learn more about prime and composite numbers

Factorization is breaking down a number into smaller prime numbers called factors, whose product is the original number.

Method: Take the number we want to factor and draw 2 branches from it. For example $12$:

Let's ask ourselves, which $2$ numbers can we find that their product will be this number, not including the number itself and $1$.
In this example, we'll choose the numbers $3$ and $4$.
Note- we could have chosen any pair of numbers whose product is $12$ and we would still get the same result.

Let's write $3$ and $4$ under the branches like this:

Now let's ask, are $4$ and $3$ composite numbers? $4$ yes $3$ no.

Let's branch out again and write the factors in the following way:

Now let's continue to ask ourselves -
$2$ is it a prime number?
Yes.

What did we get?
If we break down $12$ into prime factors,
we get that:
$2\cdot2\cdot3=12$
These are the prime factors of $12$.

Click here to learn all the ways to factor into prime numbers.

Divisibility rules by $2$

A number is divisible by $2$ if its ones digit is even – divisible by $2$ without a remainder.
For example:
The number $992$
The ones digit $2$ is even and therefore the number $992$ is divisible by $2$ without a remainder.

Divisibility rules for $4$

First Method - A number is divisible by $4$ if its last two digits form a number that is divisible by $4$.
For example, the number $7816$
The last $2$ digits are $16$ which is divisible by $4$ without a remainder, therefore 7816 is divisible by $4$ without a remainder.

Second way - multiply the tens digit by $2$ and add to the result the ones digit. If the number we got is divisible by $4$ then the original number is also divisible by 4.

For example:
The number $7816$
We multiply the tens digit $1$ by $2$ to get $2$. To this result we add the ones digit $6$ to get $8$.
$8$ is divisible by $4$ and therefore $7816$ is also divisible by $4$ without a remainder.

Divisibility rules by $10$

A number is divisible by $10$ if its ones digit is $0$.
For example:
The number $866,590$
is divisible by $10$ without a remainder because its ones digit is $0$.

Click here to learn more about divisibility rules by $2$, by $4$ and by $10$

Important reminder: What is digit sum?

The result of adding all the digits that make up the number.
For example: the sum of digits of the number $391$ is:
$3+9+1=13$
$13$.

Divisibility rules by $3$

A number is divisible by $3$ if the sum of its digits is divisible by $3$.
For example:
The number $915$
If the sum of its digits is divisible by $3$, then the original number is also divisible by $3$.
Let's check:
$9+5+1=15$
$15$ is divisible by $3$ without a remainder therefore $915$ is divisible by $3$ without a remainder.

Divisibility rules by $6$

A number is divisible by $6$ if it is even and also divisible by $3$.
For example:
The number $414$
Let's check both conditions:
Is it even? Yes.
Is it divisible by $3$? According to the sum of digits, yes.
Therefore it is divisible by $6$.

Divisibility rules for $9$

A number is divisible by $9$ if the sum of its digits is divisible by $9$.
For example:
The number $423$
If the sum of its digits is divisible by $3$, then the original number is also divisible by $3$.
Let's check:
$4+2+3=9$
$9$ is divisible by $9$ without a remainder therefore $423$ is divisible by $9$ without a remainder.

Click here to learn more about divisibility rules by $3$, by $6$ and by $9$