Final answer:
The most important sector of California's economy during the 16th and 19th centuries was the gold mining sector, driven by the California Gold Rush in 1848.
Step-by-step explanation:
The most important part of California's economy during the 16th and 19th centuries was the gold mining sector. The discovery of gold in California in 1848, known as the California Gold Rush, attracted thousands of people from all over the world who hoped to strike it rich.
The influx of settlers led to the establishment of towns and the growth of businesses such as saloons, stores, and brothels. This sector played a significant role in shaping the economy and development of California during that time period.