A quantity that multiplies another quantity is called a factor of their product.
A quantity can be multiplied by another quantity and their product forms another quantity. Mathematically, each quantity that involves in the multiplication is called a factor of their product.
It is a basic concept, whereas it has significance in mathematics. If you are new to factors, you can easily know what a factor really is, by some simple arithmetic examples as follows. It helps you to use the concept of factors in higher mathematics.
$2 \times 3$
$\implies$ $2 \times 3$ $\,=\,$ $6$
In this example, $2$ and $3$ are two numbers and they are involved in multiplication. The product of numbers $2$ and $3$ is equal to $6$.
Therefore, the numbers $2$ and $3$ are called the factors of $6$.
Now, let’s look at another arithmetic example.
$4 \times 5 \times 7$
$\implies$ $4 \times 5 \times 7$ $\,=\,$ $140$
In this example, $4,$ $5$ and $7$ are numbers, involved in multiplication and their product is equal to $140$.
Therefore, the numbers $4,$ $5$ and $7$ are called the factors of $140$.
The above two examples cleared you to know what a factor is in mathematics. Now, let’s learn more about a factor further from the following example.
$3 \times 5$ $\,=\,$ $15$
According to above examples, you can easily say that the numbers $3$ and $5$ are factors of $15$. Yes, you are absolutely correct.
In other words, a number can be a factor of another number, if it divides another number completely. Let’s to prove it by dividing the number $15$ with $3$.
$\require{enclose}
\begin{array}{rll}
5 && \hbox{} \\[-3pt]
3 \enclose{longdiv}{15}\kern-.2ex \\[-3pt]
\underline{-~~~15} && \longrightarrow && \hbox{$3 \times 5 = 15$} \\[-3pt]
\phantom{00} 0 && \longrightarrow && \hbox{No Remainder}
\end{array}$
There is no remainder when the number $3$ divides $15$, which means the number $3$ divides $15$ completely. So, the number $3$ is called a factor of $15$.
Similarly, it can be proved that the number $5$ is also a factor of $15$.
The fundamental definition of a factor and the above three simple examples helped you to understand the concept of a factor in mathematics.
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