What characteristic of metals is primarily associated with their capacity to stretch without breaking?

Ductility is the correct answer because it refers to the ability of a metal to undergo significant deformation before rupture or fracture. When a metal is ductile, it can be stretched into wires or shaped in various forms without breaking, which makes it particularly valuable in applications where flexibility and resilience under stress are required.

In contrast, brittleness indicates a material's tendency to break or shatter without significant deformation. Hardness measures a material's resistance to deformation, typically under compressive force, but does not relate to its ability to stretch. Toughness describes a material's ability to absorb energy and plastically deform without fracturing, which encompasses both strength and ductility, but it is ductility specifically that highlights the capacity to stretch. Thus, ductility stands out as the characteristic that defines how a metal can stretch without breaking.