3729

3729 is a positive integer that appears in various mathematical contexts. In number theory, it is notable for being the product of three distinct primes: 3, 11, and 113. Consequently, its prime factorization is 3729 = 3 × 11 × 113, and it is a square-free, odd composite number. It has eight positive divisors: 1, 3, 11, 33, 113, 339, 1243, and 3729.

As a composite of distinct primes, 3729 is not a perfect power and does not belong to several simple integer sequences such as squares or cubes. Its divisibility properties are straightforward: it is divisible by 3, 11, and 113, and hence by their combinations as reflected in its divisor set.

In terms of numeral representations, 3729 is written as 111001001001 in binary and 0x0E91 in hexadecimal. In Roman numerals, it can be expressed as MMMDCCXXIX.

If interpreted as a year, 3729 could refer to a time in the distant past (3729 BCE) or in the distant future (3729 CE). There is no widely cited historical event uniquely associated with the year 3729 in standard reference works, though events would depend on the calendar system and region considered.

In summary, 3729 is an eight-divisor, square-free composite number with prime factors 3, 11, and 113, and it admits common representations across several bases and numeral systems.