Since both 66 and 78 are divisible by 2, factor out 2 from the sum 66+78 using the distributive property:
[tex]\begin{gathered} 66+78=2(\frac{66}{2}+\frac{78}{2}) \\ =2(33+39) \end{gathered}[/tex]
Since both 33 and 39 are divisible by 3, factor out 3 from 33+39 using the distributive property:
[tex]\begin{gathered} 2(33+39)=2\times3(\frac{33}{3}+\frac{39}{3}) \\ =6(11+13) \end{gathered}[/tex]
Since 11 and 13 are prime numbers, then the gcf of 66 and 78 is 6.
Therefore:
[tex]\begin{gathered} 66+78=6(11+13) \\ =6(24) \\ =144 \end{gathered}[/tex]
