Help me ID this cactus please.

[mistergsf]

We've had this cactus I think since 2004 and it's been growing like crazy in our light well for the past 3 years. To me it was just a "normal" cactus that I saved from a table centerpiece but now I would like to know what it is with your help.

Thanks!

PS
When I first got it, it was barely 2" tall and 3" wide and looked like Mickey Mouse.

[Kamos]

Opuntia microdasys albispina

[mistergsf]

Thank you, Kamos!!!

[greenknight]

That's what it is, all right - and a very happy looking specimen, too!

[mistergsf]

Thanks greenknight! Very pleasing to have something thriving without much effort on my part. It has been dropping buds lately. There's a peek of one at the bottom right. Is there a wrong or right time for me to transfer a bud into another pot and start another?

[greenknight]

Anytime during the growing season will work for starting cuttings, as long as you can provide warmth. Right now would be perfect - in the Northern Hemisphere, that is.