Question

What is gcf and the distributive property to find the sum 66 + 78

Answer 1

Since both 66 and 78 are divisible by 2, factor out 2 from the sum 66+78 using the distributive property:

`\begin{gathered} 66+78=2((66)/(2)+(78)/(2)) \\ =2(33+39) \end{gathered}`

Since both 33 and 39 are divisible by 3, factor out 3 from 33+39 using the distributive property:

`\begin{gathered} 2(33+39)=2*3((33)/(3)+(39)/(3)) \\ =6(11+13) \end{gathered}`

Since 11 and 13 are prime numbers, then the gcf of 66 and 78 is 6.

Therefore:

`\begin{gathered} 66+78=6(11+13) \\ =6(24) \\ =144 \end{gathered}`