\myheading{Coprime numbers}

Coprime numbers are the 2 or more numbers which don't have any common divisors.
In mathematical lingo, the \ac{GCD} of all coprime numbers is 1.

3 and 5 are coprimes. So are 7 and 10. So are 4, 5 and 9.

Coprime numbers are the numerator and denominator in fraction which cannot be reduced further (irreducible fraction).
For example, $\frac{130}{14}$ is $\frac{65}{7}$ after reduction (or simplification), 65 and 7 are coprime to each other, but 130 and 14 are not (they has 2 as common divisor).

One application of coprime numbers in engineering is to make number of cogs on cogwheel and number of chain elements on chain to be coprimes.
Let's imagine bike cogwheels and chain:

\begin{figure}[H]
\centering
\includegraphics[scale=0.7]{prime/1.png}
\caption{The picture was taken from www.mechanical-toys.com}
\end{figure}

If you choose 5 as number of cogs on one of cogwhell and you have 10 or 15 or 20 chain elements, each cog on cogwheel will meet some set of the same chain elements.
For example, if there are 5 cogs on cogwheel and 20 chain elements, each cog will meet only 4 chain elements and vice versa: 
each chain element has its \textit{own} cog on cogwheel.
This is bad because both cogwheel and chain will run out slightly faster than if each cog would interlock every chain elements at some point.
To reach this, number of cogs and chain elements could be coprime numbers, like 5 and 11, or 5 and 23.
That will make each chain element interlock each cog evenly, which is better.