The safest thing to do is shut off power to the outlet, although you don't have to. But its easier than you think. If you want to play it safe, plug a radio into the outlet and turn it up loud enough so you can hear it from the breaker box. Make sure no computers, tvs, and other sensitive electronics are on...even though they go through the same thing whenever the power cuts out, but why add to the cumulative wear and tear. As you listen to the radio, cycle each breaker on and off slowly until you hear the radio go off. Then you know the power is out. Its most likely NOT one of the large or doubled switches in the breaker, those are for the A/C, or the clothes dryer.
If you really dont want to shut power, use a needlenose plyer with rubber grips. Even though you probably wouldnt get a shock pulling the prong out of only one side of the outlet, there is still a "bit" of risk, because if the broken off piece is on the hot side, you could theoretically be a "ground" and the electricity "could" flow through you to the ground, but that would in reality only happen if you were standing in a puddle of water wearing non insulated shoes.
I know which breaker it's on. I just hate doing that stuff. It's a mental block like some males have against cooking. I know it's stupid, but to me this is something for a man to do. Wanna take a ride "cross the river to the Jersey side"? LOL j/k I'll manage.