How do u find the greatest common factor between two numbers using the distributive property

Question

12+80. They are telling me to use the distributive property to find the greatest common factor of the two. 

Answer 1

I woiuld not say that 'using the distributive property' is key to this; the key is to write each number in its prime factorization, and then to FACTOR OUT as much as you can (*common factors):

 

12 = 3(2²)          80 = 5(2⁴)

 

By inspection, one should see that the GCF is 2 squared, which is four, so

this expression is equivalent to 4(3+5•2²) = 4(3+20) = 4(23) = 92.

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