Explain, why (𝟔×𝟓×𝟒×𝟑×𝟐×𝟏)+𝟓 is a composite number ?

 

Numbers which have atleast one factor other than $\mathrm{𝟏}$ and the number itself are called composite numbers.

Example: $4,6,8,...$

$=(\mathrm{𝟔}\times \mathrm{𝟓}\times \mathrm{𝟒}\times \mathrm{𝟑}\times \mathrm{𝟐}\times \mathrm{𝟏})+\mathrm{𝟓}$

$=(\mathrm{𝟔}\times \boxed{{\displaystyle \mathrm{𝟓}}}\times \mathrm{𝟒}\times \mathrm{𝟑}\times \mathrm{𝟐}\times \mathrm{𝟏})+\boxed{{\displaystyle \mathrm{𝟓}}}\times \mathrm{𝟏}$

$=\boxed{{\displaystyle \mathrm{𝟓}}}\times [(\mathrm{𝟔}\times \mathrm{𝟒}\times \mathrm{𝟑}\times \mathrm{𝟐}\times \mathrm{𝟏})+\mathrm{𝟏}]$

It shows that $\mathrm{𝟓}$ is a factor of given number, other than $\mathrm{𝟏}$ and the number itself.

So, $(\mathrm{𝟔}\times \mathrm{𝟓}\times \mathrm{𝟒}\times \mathrm{𝟑}\times \mathrm{𝟐}\times \mathrm{𝟏})+\mathrm{𝟓}$ is a composite number.