a)
[tex]4=\textcircled{2} \times \textcircled{2} \\
12=\textcircled{2} \times \textcircled{2} \times 3 \\
GCF(4,12)=2 \times 2=4 \\ \\
4d+12e=4 \times d+4 \times 3e=4(d+3e)[/tex]
b)
[tex]18=\textcircled{2} \times \textcircled{3} \times 3 \\
30=\textcircled{2} \times \textcircled{3} \times 5 \\
GCF(18,30)=2 \times 3=6 \\ \\
18x+30y=6 \times 3x + 6 \times 5y=6(3x+5y)[/tex]
c)
[tex]21=3 \times \textcircled{7} \\
28=2 \times 2 \times \textcircled{7} \\
GCF(21,28)=7 \\ \\
21a+28y=7 \times 3a+4 \times 4y=7(3a+4y)[/tex]
d)
[tex]24=\textcircled{2} \times \textcircled{2} \times \textcircled{2} \times 3 \\
56=\textcircled{2} \times \textcircled{2} \times \textcircled{2} \times 7 \\
GCF(24,56)=2 \times 2 \times 2=8 \\ \\
24f+56g=8 \times 3f+8 \times 7g=8(3f+7g)[/tex]
