A quantity that multiplies another quantity is called a factor of their product.
At your beginner level, you learn the concept of factors from arithmetic. If you are a beginner, let’s learn firstly what a factor really is by numbers.
$2 \times 3$ $\,=\,$ $6$
The numbers $2$ and $3$ both divide $6$ completely because the number $6$ is formed by the product of $2$ and $3$. So, the numbers $2$ and $3$ are called the factors of $6$.
If you have already studied the concept of factors in arithmetic, let’s upgrade our knowledge on factors to higher level. In advanced level, the quantities are not denoted by numbers because they are unknown. So, a quantity is generally written in the form an expression.
When an expression is multiplied by another expression and their product is also a mathematical expression. It can be divided by both expressions completely because the expression is formed by the product of two or more expressions. So, each expression is called a factor of their product.
Now, let’s know the concept of factors further with some understandable examples.
$x \times (x-4)$ $\,=\,$ $x^2-4x$
$x$ and $x-4$ are two expressions, whereas their product is $x^2-4x$. So, $x$ and $x-4$ both can divide the expression $x^2-4x$ completely.
Therefore, the expressions $x$ and $x-4$ are called the factors of $x^2-4x$.
Now, let’s have a look at some more examples to know the concept of factors in advanced mathematics.
$6 \times (x+1) \times \sin{x}$ $\,=\,$ $6x\sin{x}+6\sin{x}$
$6$ is a number, $x+1$ and $\sin{x}$ are two expressions, which denote two unknown quantities.
The product of $6$, $x+1$ and $\sin{x}$ is $6x\sin{x}+6\sin{x}$. So, the expression $6x\sin{x}+6\sin{x}$ can be divided completely by $6$, $x+1$ and $\sin{x}$.
Mathematically, the quantities $6$, $x+1$ and $\sin{x}$ are called the factors of $6x\sin{x}+6\sin{x}$.
Now, you have clearly learned the concept of factors in higher mathematics from its definition and understandable examples.
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