390400

390400 is a natural number that sits between 390399 and 390401. In number theory, it is notable for its factorization and its decimal properties rather than for any particular cultural or historical significance.

The prime factorization of 390400 is 2^8 × 5^2 × 61. This shows the number is even and composite, with a mixed prime structure. From this factorization, the number has (8+1)(2+1)(1+1) = 54 positive divisors. Its divisibility makes it a multiple of 100, since the exponent of 2 is at least 2 and the exponent of 5 is at least 2, and 390400 / 100 = 3904. It can also be expressed as 61 × 6400 or 6100 × 64, illustrating how the divisors arise from combinations of the prime factors.

In decimal form, 390400 ends with two zeros, reflecting the factor of 10 coming from 2^2 and 5^2 in its prime factorization. This trailing-zero property is a direct consequence of those exponents and means the number is divisible by 100 but not by 1000.

As a mathematical object, 390400 serves as an example of a relatively highly composite-like structure within a relatively small range, illustrating how mixed prime factors influence divisibility and the number of divisors. There are no widely known constants or famous theorems specifically associated with this number beyond its general factorization properties.