111111111111

111111111111 is the decimal representation of a repunit number, specifically a base-10 repunit of length twelve. A repunit is a number composed of repeated copies of the digit 1, and in general Rn denotes the number formed by n consecutive ones in base 10. For base-10, Rn can be written as (10^n − 1)/9; thus 111111111111 = (10^12 − 1)/9.

As a 12-digit repunit, 111111111111 is a composite number. Its value can be factored as 3 × 7 × 11 × 13 × 37 × 101 × 9901, with all factors prime. The factor 9901 is itself prime. This factorization demonstrates that the number has multiple distinct prime factors and is not a prime power.

Divisibility properties for repunits also apply here. Since 12 is divisible by 3, 4, and 6, the number is divisible by the shorter repunits R3 = 111, R4 = 1111, and R6 = 111111. Indeed, 111111111111 is divisible by each of these repunits, reflecting the standard divisibility relationships among repunits when the length divides the overall length.

In mathematical contexts, 111111111111 serves as an example of a long base-10 repunit with a well-known, nontrivial prime factorization. It is studied in number theory as part of the broader family of repunits and their factorization properties.