The number $12$ can be written as the product $\blue{3\times 4}$. We call $\blue{3\times 4}$ a $\blue{\textbf{factorization}}$ of $12$, since we factorized $12$ into two factors that are both smaller than $12$.

The product $\red{12\times 1}$ is $\red{\textbf{not}}$ a factorization of $12$, because the factor $12$ is not smaller than $12$. In this case, we did not factorize $12$.

Not every number can be factorized. For example, it does not work with the number $7$.

If we write a positive integer as a product of smaller positive integers,
this is known as a $\blue{\textbf{factorization}}$ of that integer

Examples

$$\begin{array}{rcl} \red{1 \times 12} &=& 12 \\ \blue{2 \times 6} &=& 12 \\ \blue{3 \times 4} &=& 12 \\ \blue{4 \times 3} &=& 12 \\ \blue{6 \times 2} &=& 12 \\ \red{12 \times 1} &=& 12 \end{array}$$