465584400 has 180 divisors, whose sum is σ = 1686255168. Its totient is φ = 118736640.

The previous prime is 465584387. The next prime is 465584401. The reversal of 465584400 is 4485564.

It is a tau number, because it is divible by the number of its divisors (180).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (465584401) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 79989 + ... + 85611.

Almost surely, 2^465584400 is an apocalyptic number.

465584400 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 465584400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (843127584).

465584400 is an abundant number, since it is smaller than the sum of its proper divisors (1220670768).

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

465584400 is a wasteful number, since it uses less digits than its factorization.

465584400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5670 (or 5656 counting only the distinct ones).

The product of its (nonzero) digits is 76800, while the sum is 36.

The square root of 465584400 is about 21577.4048485910. The cubic root of 465584400 is about 775.0555076441.

The spelling of 465584400 in words is "four hundred sixty-five million, five hundred eighty-four thousand, four hundred".