Take the prime factorizations of each given number. For example, in (a) we have
[tex]\mathrm{gcf}(40,60)=20[/tex]
because we can write [tex]40=2^3\cdot5[/tex] and [tex]60=2^2\cdot3\cdot5[/tex], and the largest number that we can divide both numbers by with no remainder is [tex]2^2\cdot5=20[/tex]. When we do this division, we have [tex]\dfrac{2^3\cdot5}{2^2\cdot5}=2[/tex] and [tex]\dfrac{2^2\cdot3\cdot5}{2^2\cdot5}=3[/tex]. The numbers 2 and 3 share no common factors.
Then for (b),
[tex]\mathrm{gcf}(24,36)=\mathrm{gcf}(2^3\cdot3,2^2\cdot3^2)=2^2\cdot3=12[/tex]
and for (c),
[tex]\mathrm{gcf}(18,45,90)=\mathrm{gcf}(2\cdot3^2,3^2\cdot5,2\cdot3^2\cdot5)=3^2=9[/tex]
