456504000 has 224 divisors, whose sum is σ = 1574816256. Its totient is φ = 116300800.

The previous prime is 456503981. The next prime is 456504007. The reversal of 456504000 is 405654.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is not an unprimeable number, because it can be changed into a prime (456504007) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 551587 + ... + 552413.

Almost surely, 2^456504000 is an apocalyptic number.

456504000 is a gapful number since it is divisible by the number (40) 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 456504000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (787408128).

456504000 is an abundant number, since it is smaller than the sum of its proper divisors (1118312256).

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

456504000 is a wasteful number, since it uses less digits than its factorization.

456504000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 880 (or 860 counting only the distinct ones).

The product of its (nonzero) digits is 2400, while the sum is 24.

The square root of 456504000 is about 21365.9542262919. The cubic root of 456504000 is about 769.9836956125.

Adding to 456504000 its reverse (405654), we get a palindrome (456909654).

The spelling of 456504000 in words is "four hundred fifty-six million, five hundred four thousand".