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An archaeologist finds two pottery shards with markings indicating their ages. The first shard is dated to be 84 years old and the second to be 126 years old. What is the greatest common factor of these two ages?
To find the greatest common factor (GCF) of 84 and 126, we first determine their prime factorizations:
\[ 84 = 2^2 \times 3 \times 7 \]

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