My iPhone 6 won't pair with an Apple bluetooth keyboard. Tried 3, all failed.

I'm trying to pair an Apple bluetooth keyboard with my iPhone 6. It detects the keyboard, but the pairing is always unsuccessful (error message: "make sure keyboard is turned on, in range and is ready to pair"). The keyboard is turned on, a foot away from the iPhone, and ready to pair. Tried with three different keyboards, all failed. What's going on?