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Assuming you're looking for the state with the greatest north-south distance, the answer is Alaska. From its northernmost latitude to its southernmost latitude is a difference of over 20°, equating to about 1394 miles. That's more than the distance from the southern tip of California to the northern tip of Washington state.

If you meant from top to bottom, the answer would still be Alaska, since the highest elevation in the United States is the summit of Mt. McKinley in Alaska.

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