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