6729

6729 is a natural number that sits between 6728 and 6730. In mathematics it is notable for being a semiprime, meaning it can be written as the product of exactly two prime numbers.

Its prime factorization is 6729 = 3 × 2243, with 2243 being a prime number. Consequently, the divisors of 6729 are 1, 3, 2243, and 6729, giving it four positive divisors. The sum of all divisors is 8976, so the sum of proper divisors is 2247. Since 2247 is less than 6729, 6729 is a deficient number.

The Euler totient function for 6729 is φ(6729) = (3 − 1)(2243 − 1) = 2 × 2242 = 4484. This reflects the number of integers up to 6729 that are relatively prime to 6729.

Because 6729 = 3 × 2243, where 3 ≡ 3 mod 4, the number is not expressible as a sum of two squares. In general, a product of a prime congruent to 3 mod 4 with odd exponent cannot be written as a^2 + b^2.

As a semiprime, 6729 serves as a simple example in discussions of factorization and related number-theoretic concepts. Its small size makes it useful for illustrative problems in elementary number theory, cryptography, and primality testing demonstrations, even though it has no particular cryptographic application by itself.