Marina,
Those values don't look like UTM. If the data's in the US, they could be State Plane instead. If the data's scattered across, even a state (let alone multiple states), you may have to figure out which zone each one is in first. Ouch. UTM X coordinates should be between 200000 and 800000 meters, while in the contiguous US, Y values are between 2.5 million and 5.5 million meters. I didn't spot an obvious state plane zone that matched 2million,2million either.
If you can post approximately where the data is located, I can see if I can find a matching coordinate system. You can do this yourself by adding a base map/other data to ArcMap and setting the data frame's coordinate system to the one you want to check. Make sure the display units match the coordinate system and just read off the coordinates from the status bar (at bottom right of map).
EDIT: You said that the data's in Canada, above Idaho. Is it in BC or Alberta? We have a few provincial coordinate systems, but they're generally putting the data pretty far North. Nearest major feature?
Thanks!
Melita