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Draw a Venn diagram. Let circle 1 be the factors of 30, circle 2 be the factors of 40 and circle 3 be the factors of 48. Put the numbers 5 and 10 in the space where 1 and 2 intersect. Put the numbers 4 and 8 in the space where 2 and 3 intersect. Put the numbers 3 and 6 in the space where 1 and 3 intersect. Put the numbers 1 and 2 in the space where all three intersect. That leaves 15 and 30 in Circle 1, 20 and 40 in circle 2 and 12, 16, 24, 48 in circle 3. The GCF is 2.
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