My dad has Team Fortress 2, and he let me install it on my computer, but it is still under his username and I can't play it with my Steam account. If I got Garry's Mod on my account, could I play Garry's Mod without having to buy Team Fortress 2, or do I need to buy it on my Steam account?

I'm fairly sure you have to have the game under the same steam account, sorry.

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Edit:
You may want to ask here for further confirmation though.

i recomend getting half life 2 and garrysmod togehter then purchase episode 1 and 2 thats what i have and i have tf2 for the extra props

i think that you just need the game on your computer for gmod to work you dont have to buy it on your account

My opinion is that you have to have a source game (example:tf2,portal,hl2,hl2dm)
installed on your gmod account for it to work,