Kahili Ginger question

I recently pried my Kahili Ginger out of the pot it had been growing in for 2 years and found huge rhizomes, like bunches of sweet potatoes all hooked together.

I was looking for information about dividing the rhizomes and really can't find a thing online.
Some of my questions:
How do you divide potato like rhizomes, can you cut them into pieces as long as there is an eye on each section?
I noticed my ginger never re-blooms on the same stock, but the foliage doesn't really die, should I cut it to the ground after the bloom is finished?
Thanks
Dovey

I read a little and it said that they start from a small piece of rhizome with an eye. If you decide to trade a small piece let me know. I would cut them back after the folliage dies.