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

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