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First factor the each term in the expression.

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44x3 2 · 2 · 11 · x · x · x

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24x2 2 · 2 · 2 · 3 · x · x

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The GCF is the product of the common prime factors in each term.

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GCF = 2 · 2 · x · x = 4x2\"\"

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The greatest common factor of 44x3and 24x2 is 4x2.