506400 has 72 divisors (see below), whose sum is σ = 1656144. Its totient is φ = 134400.

The previous prime is 506393. The next prime is 506417. The reversal of 506400 is 4605.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 506400.

It is an unprimeable number.

506400 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 2295 + ... + 2505.

It is an arithmetic number, because the mean of its divisors is an integer number (23002).

2⁵⁰⁶⁴⁰⁰ is an apocalyptic number.

506400 is a gapful number since it is divisible by the number (50) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 506400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (828072).

506400 is an abundant number, since it is smaller than the sum of its proper divisors (1149744).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

506400 is a wasteful number, since it uses less digits than its factorization.

506400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 234 (or 221 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 15.

The square root of 506400 is about 711.6178749863. The cubic root of 506400 is about 79.7072634563.

The spelling of 506400 in words is "five hundred six thousand, four hundred".