we know that
\(270=2*3^{3} *5\\180=2^{2}*3^{2}*5\)
Find the Greatest Common Factor (GCF)
The GCF is equal to------> \(2*3^{2}*5=90\)
therefore
the answer part a) is
the greatest number of packs she can make is \(90\)
Find the number of red pens in each pack
Divide the total number of red pens by the total number of packs
\(\frac{180}{90}=2\ red\ pens\)
Find the number of blue pens in each pack
Divide the total number of blue pens by the total number of packs
\(\frac{270}{90}=3\ blue\ pens\)
therefore
the answer part b) is
There are \(2\ red\ pens\) in each pack
There are \(3\ blue\ pens\) in each pack
