1. Condition: The condition of the coin is one of the most critical factors in determining its value. Coins in mint state (MS) or uncirculated (UNC) condition, with no signs of wear or damage, are generally more valuable than circulated coins.
2. Rarity: The rarity of the 1791 quarter also plays a role in its value. The first quarter dollar minted by the United States Mint was in 1796. However, a handful of pattern coins were produced in 1792, and these are extremely rare and highly sought after by collectors. The 1792 pattern quarter is considered one of the rarest US coins and can command a very high price.
3. Grade: The grade assigned to the coin by a reputable third-party grading service like the Professional Coin Grading Service (PCGS) or Numismatic Guaranty Corporation (NGC) also affects its value. Coins graded MS-65 or higher are generally considered to be in excellent condition and are more valuable than coins with lower grades.
4. Numismatic Value: Some 1791 US quarters may have special historical significance, such as being a trial strike, a proof, or having been part of a specific collection or hoard. These coins can have additional numismatic value beyond their base metallic value.
Given the scarcity and historical significance of 1791 US quarters, their value can vary from a few thousand dollars to hundreds of thousands of dollars, depending on the factors mentioned above. It's recommended to consult with an experienced numismatist or coin expert to get an accurate appraisal of a specific 1791 US quarter.