31329

31329 is a natural number that sits between 31328 and 31330. It is notable for being a perfect square: 31329 = 177^2. This also gives its prime factorization as 3^2 × 59^2, since 177 = 3 × 59. Consequently, 31329 is divisible by 3 and by 9, and the sum of its digits is 18, confirming divisibility by 9.

As a square number, 31329 is the square of the integer 177, making it the 177th square number in the sequence of perfect squares. Its square root is 177, and the only real numbers x satisfying x^2 = 31329 are x = 177 or x = -177 (when considering all real solutions).

In mathematical contexts, 31329 exemplifies several properties of squares: it is an odd, composite number with a factorization that consists entirely of squared primes. It also demonstrates how the digit sum criterion relates to divisibility by 9.

Beyond pure mathematics, five-digit numbers like 31329 can appear as identifiers in various systems, such as postal codes, catalog numbers, or model numbers. However, this article focuses on the numerical and arithmetic properties of the integer 31329.