What is the greek word of hygiene?

There isn't one single Greek word that perfectly translates to "hygiene" in the modern sense. The concept evolved over time. However, words related to cleanliness and health from which the concept derives include:

* υγεινή (hygiene): This is the modern Greek word for hygiene, but it's a loanword derived from the French "hygiène," which itself comes from the Greek word below.

* ὑγιεινός (hygieinos): This Greek word means "healthy" or "wholesome," relating to the state of being healthy, which is a core component of hygiene. It's derived from Ὑγεία (Hygieia), the goddess of health and cleanliness in Greek mythology.

So while there's no direct ancient Greek equivalent to the modern English "hygiene," ὑγιεινός (hygieinos) and Ὑγεία (Hygieia) are the closest etymological roots.