505440

505,440 is a positive integer that lies between 505,439 and 505,441. It is an even number and a multiple of 10, reflecting its factors in decimal notation.

Its prime factorization is 505,440 = 2^5 × 3^5 × 5 × 13. Equivalently, 505,440 = 6^5 × 65, since 6^5 = 2^5 × 3^5 and 65 = 5 × 13. This makes the number highly composite in its construction, combining small primes raised to moderate powers.

505,440 has 144 positive divisors, calculated from its factorization as (5+1)(5+1)(1+1)(1+1) = 6 × 6 × 2 × 2. The sum of all divisors is σ(505,440) = 63 × 364 × 6 × 14 = 1,926,288. Since σ(n) > 2n, the number is abundant; its abundance is 1,926,288 − 2 × 505,440 = 915,408. It is not a perfect square (the square root lies between 710 and 711, with 711^2 = 505,521).

In base representations, 505,440 equals 0x7B660 in hexadecimal. The decimal digits include recurring 5 and 4, and the number is divisible by 9, 5, and 13, among others, due to its prime factorization.

Contextually, 505,440 is primarily of interest in number theory and combinatorial calculations involving factorization, divisor counts, and modular arithmetic rather than serving as a widely cited constant or identifier.

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