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?

Mon, 04 May 2026 01:20:59 +0000

An Archaeologist Discovers Two Pottery Shards: Revealing Ages and the Greatest Common Factor In a fascinating archaeological find, researchers uncovered two ancient pottery shards that offer valuable insights into the cultures of the past. Among the key discoveries was a detailed examination of the markings left on the fragments, which helped determine their relative ages—84 years and 126 years. But beyond just dating these remnants, the team uncovered a meaningful mathematical detail: the greatest common factor (GCF) of 84 and 126. Understanding this GCF not only supports the historical timeline but also reveals patterns in craftsmanship, trade, and cultural practices of the time. Let’s explore how this number connects to the past—and why it matters. ### Dating the Shards: A Window into the Past