MoMath + Wolfram

Funding for this project generously provided by Overdeck Family Foundation


Cataldi's Divisor Table

Oldest divisor table, giving divisors for numbers up to 750

Cataldi wrote the first divisor table in 1588, publishing a table of divisors up to 750 (extended to 800 in a supplement) in 1603.

Cataldi's Divisor Table

The oldest divisor table is due to Cataldi, who gave a list of the divisors of all numbers to 750 (extended to 800) in connection with his study of perfect numbers. The work was composed in 1588 and published in Bologna in 1603. Cataldi proved with the help of his table that Mersenne numbers 2^17 - 1 and 2^19 - 1 were prime and asserted that exponents 23, 29, 31, 37 also generated perfect numbers. The assertion was later proven false (with the exception of 31) by Fermat and Euler.

Artifact dimensions

5.8 in. × 7.8 in. (52 pages)

Artifact origin

Bologna, Italy


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.
  • Cataldi, A. Trattato de’ numeri perfetti. Bologna, Italy: presso gli heredi di Giouanni Rossi, 1603.