393129

393129 is a natural number that sits between 393128 and 393130. In mathematical terms, it has several notable properties that make it a point of interest for number theory.

Most prominently, 393129 is a perfect square, equal to 627 squared. Its prime factorization is 3^2 × 11^2 × 19^2, which confirms that it is the square of the product 3 × 11 × 19 = 627. Consequently, the divisors of 393129 come in complementary pairs around the square root, and every divisor occurs with even multiplicity in the factorization.

As a result of its prime structure, 393129 is divisible by 9 (since the sum of its digits is 27, a multiple of 9), as well as by 121 (11^2) and by 361 (19^2). Indeed, 393129 = 9 × 43681 = 121 × 3249 = 361 × 1089, all of which are squares themselves. The digital sum of 393129 is 27, giving a digital root of 9, which is consistent with its divisibility by 9.

In summary, 393129 is a square number with square root 627, and its prime factorization is composed entirely of squared primes (3^2, 11^2, and 19^2). These properties make it a straightforward example of a composite square with a rich, explicit factor structure.