# Factors of 16

## Factors

$1$, $2$, $4$, $8$ and $16$ are the factors of sixteen. ### Factorization

The number sixteen is a real natural number. It should be factorised to learn how to factorize the number $16$ and also to know which natural numbers are the factors of sixteen.

#### Divide 16 by 1

Let’s divide the number sixteen by the number one firstly to find their quotient.

$16 \,\div\, 1$

$\implies$ $\dfrac{16}{1} \,=\, 16$

The number $1$ completely divides the number $16$. Therefore, the quotient of $16$ divided by $1$ is equal to $16$.

Likewise, the number $16$ also divides the number $16$ completely.

$16 \,\div\, 16$

$\implies$ $\dfrac{16}{16} \,=\, 1$

The quotient of $16$ divided by $16$ is equal to $1$. Now, the number $16$ can be written as a product of the natural numbers $1$ and $16$.

$\,\,\,\therefore\,\,\,\,\,\,$ $1 \times 16$ $\,=\,$ $16$

Therefore, the numbers $1$ and $16$ are called the factors of the number $16$.

#### Divide 16 by 2

Now, divide the number sixteen by the number two to calculate their quotient.

$16 \,\div\, 2$

$\implies$ $\dfrac{16}{2} \,=\, 8$

The number $2$ completely divides the number $16$. So, the quotient of $16$ divided by $2$ is equal to $8$.

Similarly, the number $8$ also completely divides the number $16$.

$16 \,\div\, 8$

$\implies$ $\dfrac{16}{8} \,=\, 2$

The quotient of $16$ divided by $8$ is equal to $2$. Therefore, the number $16$ can be expressed as a product of the numbers $2$ and $8$.

$\,\,\,\therefore\,\,\,\,\,\,$ $2 \times 8$ $\,=\,$ $16$

Therefore, the numbers $2$ and $8$ are called the factors of a natural number $16$.

#### Divide 16 by 4

Finally, divide the number sixteen by the number four to evaluate their quotient.

$16 \,\div\, 4$

$\implies$ $\dfrac{16}{4} \,=\, 4$

The natural number $4$ completely divides the number $16$. Therefore, the quotient of $16$ divided by $4$ is equal to $4$.

Therefore, the number $16$ can be written as a product of the numbers $4$ and $4$.

$\,\,\,\therefore\,\,\,\,\,\,$ $4 \times 4$ $\,=\,$ $16$

Therefore, the numbers $4$ is called a factor of a natural number $16$.

#### Conclusion

It is evaluated that the numbers $1$ and $16$, $2$ and $8$ and $4$ are the factors of the natural number $16$. Therefore, the factors of $16$ are $1$, $2$, $4$, $8$ and $16$.

The remaining numbers $3$, from $5$ to $7$ and from $9$ to $15$ cannot completely divide the number $16$. Therefore, these numbers cannot be the factors of the number $16$.

##### Representation

The factors of $16$ is represented by $F$ subscript $16$ mathematically in algebraic form.

$F_{16}$ $\,=\,$ $\big\{1,\, 2,\, 4,\, 8,\, 16\big\}$

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