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Guldin's Factor Table

One of the oldest factor tables, giving factorizations up to 10,000

Paul Guldin made an early factor table up to 10,000 in his 1641 four-book work on mathematics and astronomy De Centro Gravitatis, extending the earlier table from Cataldi.

Guldin's Factor Table

Swiss Jesuit mathematician and astronomer Paul Guldin made a factor table of odd numbers not divisible by 10 up to 10,000 in the fourth book of his series De Centro Gravitatis in 1641. The table was captioned "tabula ultima," referring to the fact that it is the last table in the last book of his four-volume work. The motivation for the computation and inclusion of this table is not clear based on Guldin's own explanation.

Artifact dimensions

7.4 in. × 11.4 in.

Artifact origin

Vienna, Austria

Current artifact location

Linda Hall Library of Science, Engineering & Technology

Catalog number

QA444.G84 1635


Primes timeline The Sieve of Eratosthenes Cataldi's Divisor Table Guldin's Factor Table Van Schooten's Prime Table Turing's Zeta Function Machine SWAC Computes New Mersenne Primes

Interactive Content

Computational Explanation

Other Resources

Additional Reading

  • Bullynck, M. "Factor Tables 1657–1817, with Notes on the Birth of Number Theory." Revue d'Histoire des Mathematiques, Vol. 16, No. 2, pp. 133–216, 2010.
  • Guldin, P. Tabla Ultima following Book IV in De centro gravitatis: De usu centri gravitatis binarum specierum quantitatis continuae, sive de compositione et resolutione potestatum rotundarum. Vienna, Austria: Cosmerovius, pp. 393–401, 1641.

Image Credits

Linda Hall Library of Science, Engineering & Technology, Kansas City, Missouri