@divinedolphin The "pairwise relatively prime" condition is stronger than "relatively prime." For example, if two numbers have \(2\) as a common factor, but the third number doesn't, then the three numbers together are relatively prime.
Relatively prime means that there is no factor common to all numbers in the group .
Pairwise relatively prime means that if you look at all possible pairs of the numbers, there is not a pair that share a common factor.
$$ \textcolor{red}{4 \text{ } \text{ } 10}\text{ } \text{ } 7 $$
$$ \text{These are relatively prime (because 7 doesn't have 2 as a factor)} $$
$$ \textcolor{red}{4 \text{ } \text{ } 10}\text{ } \text{ } 7 $$
$$\begin{aligned}
\text{Look at them pairwise: } &\textcolor{red}{4} \text{ and } \textcolor{red}{10} \text{ are both multiples of 2 }; \\
&\textcolor{red}{4} \text{ and } 7 \text{ are not both multiples of some number,}\\
\text{ and } &\textcolor{red}{10} \text{ and } 7 \text{ are not both multiples of some number}
\end{aligned}
$$
$$ \text{These three numbers are not pairwise relatively prime. } $$
$$ \textcolor{blue}{44 \text{ } \text{ } 13 \text{ }\text{ } 25 } $$
$$ \text{ These are not all multiples of the same } x, \text{ for some number } x, \text{ so they are relatively prime} $$
$$ \textcolor{blue}{44 \text{ } \text{ } 13 \text{ }\text{ } 25 } $$
$$\begin{aligned}
\text{Look at them pairwise: } &\textcolor{blue}{44} \text{ and } \textcolor{blue}{13} \text{ are not both multiples of some number }; \\
&\textcolor{blue}{13} \text{ and } \textcolor{blue}{25} \text{ are not both multiples of some number,}\\
\text{ and } &\textcolor{blue}{44} \text{ and } \textcolor{blue}{25} \text{ are not both multiples of some number}
\end{aligned}
$$
$$ \text{These three numbers are also pairwise relatively prime.} $$