#Mathematica 14 12 bytes
Mathematica 14 12 bytes
Since built-ins are allowed, this should do it.
FindClusters
Example
FindClusters[{{4, 8}, {15, 16}, {23, 42}, {-13.37, -12.1}, {666, -666}}, 3]
{{{4, 8}, {-13.37, -12.1}}, {{15, 16}, {23, 42}}, {{666, -666}}}