My mother has had this plant for years and we have never been able to figure out what it is. Any help appreciated and thanks in advance!

Hello, I'm certainly not an expert in cacti, but it looks similar to Old Man of the Andes, which has hair similar to yours.

Looks like a moldy catus to me

THe fuzzy stuff is part of the cactus -- not mold I can see the resemblance!

It's something form the opuntia-type area.

There is a hens and chicks that has hair similar to this, but this is a cactus. Here's mine.

Thank you all for your help!

Looks like an Austrocylindopuntia vestita var cristata to my eyes, with some portion reverting into non cristate form.
It is common on cristate cactus to have some part reverting to normal form. Some time it is advised to cut off the reverted part, if it grow too fast, because sometime it can out grow the cristate form and supress it's growth. But it depends on ones preference.

Because you haven't heard that enough yet.

Thank you all for your help!

Plant ID app: Old Man Cactus (Cephalocereus senilis)
The wild population of this cactus is listed as endangered.

The ID of this plant is Austrocylindopuntia vestita var cristata. The cristata part is the fuzzy part on the bottom. The longer branches are the cactus attempting to revert to Austrocylindropuntia vestita. On these types of cactus, the only way to maintain the cristata is to cut off the reversion branches.

Give your Plant ID App a failing grade. The NGA Plant ID App is a much better choice (and always free!).

DaisyI said: The ID of this plant is Austrocylindopuntia vestita var cristata. The cristata part is the fuzzy part on the bottom. The longer branches are the cactus attempting to revert to Austrocylindropuntia vestita. On these types of cactus, the only way to maintain the cristata is to cut off the reversion branches.

Give your Plant ID App a failing grade. The NGA Plant ID App is a much better choice (and always free!).

No download, too!