Final answer:
To a remote observer, a clock nearing a black hole's event horizon will appear to slow down and virtually stop due to gravitational time dilation, although the person with the clock would not notice any change in the passage of time.
Step-by-step explanation:
When a clock approaches the event horizon of a black hole, as viewed by a remote observer, time appears to slow down significantly and seems to stop at the event horizon itself. This effect is due to the intense gravitational field of the black hole causing what is known as gravitational time dilation. The closer the clock gets to the event horizon, the more its time will dilate, and the signals it sends out will have increasingly longer intervals between them. To the remote observer, the clock will appear almost frozen as it approaches the event horizon. This is different from the perspective of someone falling into the black hole, for whom time would seem to proceed normally.