RANSOM, Kan.—The Farm Belt is hurtling toward a milestone: Soon there will be fewer than two million farms in America for the first time since pioneers moved westward after the Louisiana Purchase.

Across the heartland, a multiyear slump in prices for corn, wheat and other farm commodities brought on by a glut of grain world-wide is pushing many farmers further into debt. Some are shutting down, raising concerns that the next few years could bring the biggest wave of farm closures since the 1980s.

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