The prime factorizations of 16 and 24 are shown below. Prime factorization of 16: 2, 2, 2,2
Prime factorization of 24: 2, 2, 2, 3

Using the prime factorizations, what is the greatest common factor of 16 and 24?

(A) 2
(B) 2 ` 2
(C) 2 ` 2 ` 2
(D) 2 ` 2 ` 2 ` 2 ` 3​

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step-by-step explanation:

72 is the answer to this problem

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4