Math Doubts

What are the Factors of 4?

Factors

$1,$ $2$ and $4$ are the factors of $4$.

The number four is a natural number and also a whole number. The number $4$ represents a whole quantity in mathematics and it should be expressed as factors in some cases. Therefore, it is must for us to know the factors of four.

factors of 2

The factors of $2$ are $1$ and $2$ as per arithmetic and we should know why $1$ and $2$ are only factors of number $2$. So, let’s learn how to find the factors of $2$ in mathematics.

The number $1$ is a first natural number in mathematics. So, let’s divide the number $2$ by $1$ firstly.

Step: 1

$4 \div 1$

$=\,\,$ $\dfrac{4}{1}$

Use the long division method to divide the number $2$ by $1$ and it helps us to know about the remainder.

$\require{enclose}
\begin{array}{rll}
4 && \hbox{} \\[-3pt]
1 \enclose{longdiv}{4}\kern-.2ex \\[-3pt]
\underline{-~~~4} && \longrightarrow && \hbox{$1 \times 4 = 4$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

There is no remainder when the number $2$ is divided by $1$, it clears that the number $1$ divides $2$ completely. Therefore, the number $1$ is a factor of $2$.

Now, let’s divide the number $2$ by itself.

Step: 2

$4 \div 2$

$=\,\,$ $\dfrac{4}{2}$

Let’s use long division method one more time to know whether the number $2$ divides itself completely or not.

$\require{enclose}
\begin{array}{rll}
2 && \hbox{} \\[-3pt]
2 \enclose{longdiv}{4}\kern-.2ex \\[-3pt]
\underline{-~~~4} && \longrightarrow && \hbox{$2 \times 2 = 4$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

Step: 3

$4 \div 3$

$=\,\,$ $\dfrac{4}{3}$

Let’s use long division method one more time to know whether the number $2$ divides itself completely or not.

$\require{enclose}
\begin{array}{rll}
1 && \hbox{} \\[-3pt]
3 \enclose{longdiv}{4}\kern-.2ex \\[-3pt]
\underline{-~~~3} && \longrightarrow && \hbox{$3 \times 1 = 3$} \\[-3pt]
\phantom{00} 1 && \longrightarrow && \hbox{Remainder}
\end{array}$

Step: 4

$4 \div 4$

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

Let’s use long division method one more time to know whether the number $2$ divides itself completely or not.

$\require{enclose}
\begin{array}{rll}
1 && \hbox{} \\[-3pt]
4 \enclose{longdiv}{4}\kern-.2ex \\[-3pt]
\underline{-~~~4} && \longrightarrow && \hbox{$4 \times 1 = 4$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$

There is no remainder when the number $2$ is divided by itself, it means the number $2$ divides the same number completely. Therefore, the number $2$ is a factor of itself.

Conclusion

It has proved that the numbers $1,$ $2$ and $4$ divide the number $4$ completely. So, the numbers $1,$ $2$ and $4$ are factors of number $4$ mathematically.

Factorization

The factors of $4$ are $1,$ $2$ and $4$. The number $4$ can be expressed possibly in the following forms in terms of its factors $1,$ $2$ and $4$.

$(1).\,\,$ $4 \,=\, 1 \times 4$

$(2).\,\,$ $4 \,=\, 2 \times 2$

Representation

The factors of $2$ is expressed mathematically as follows.

$F_{4} \,=\, \{1, 2, 4\}$

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