Final answer:
Henry Hudson claimed the area now known as New York for the Netherlands due to its large supply of furs, valuable for the fur trading market at the time.
Step-by-step explanation:
The factor that encouraged Henry Hudson to claim the area now known as New York for the Netherlands was a. Its large supply of furs. While employed by the Dutch East India Company in 1609, Hudson explored the region and identified its potential for fur trading, which was a lucrative commodity at the time. The bountiful fur resources, particularly beaver pelts, provided ample reason to claim the territory for the Dutch, who later established New Netherland as a fur-trading center with its headquarters in New Amsterdam, present-day Manhattan.