3993

3993 is a natural number that lies between 3992 and 3994. It is an odd and composite integer with several notable mathematical properties.

Its prime factorization is 3 × 11^3, which means 3993 is divisible by 3 and by 11, including higher powers of 11. The complete set of positive divisors is 1, 3, 11, 33, 121, 363, 1331, and 3993. The sum of its digits is 24, so the number is divisible by 3 but not by 9.

In different numeral systems, 3993 has the representations 0xF99 in hexadecimal and 0b111110011001 in binary. In Roman numerals, it is written as MMMCMXCIII.

Further factorization forms include 3993 = 33 × 121 and 3993 = 3 × 11^3, illustrating its structure as a product of a small prime and a cube of a prime. It is neither a triangular number nor a perfect square.

Beyond pure mathematics, 3993 is commonly encountered as a numerical label or identifier in various catalogs, models, or datasets. While it does not have widely recognized historical or mathematical notoriety beyond its factorization and base representations, it serves as a representative example of a composite number with a high power of a small prime.