464810400 has 252 divisors, whose sum is σ = 1703433942. Its totient is φ = 123793920.

The previous prime is 464810393. The next prime is 464810407. The reversal of 464810400 is 4018464.

464810400 is a `hidden beast` number, since 4 + 648 + 10 + 4 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (464810393) and next prime (464810407).

It can be written as a sum of positive squares in 3 ways, for example, as 341067024 + 123743376 = 18468^2 + 11124^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (464810407) by changing a digit.

It is a polite number, since it can be written in 41 ways as a sum of consecutive naturals, for example, 582802 + ... + 583598.

Almost surely, 2^464810400 is an apocalyptic number.

464810400 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 464810400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (851716971).

464810400 is an abundant number, since it is smaller than the sum of its proper divisors (1238623542).

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

464810400 is an equidigital number, since it uses as much as digits as its factorization.

464810400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 835 (or 807 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

The square root of 464810400 is about 21559.4619598913. The cubic root of 464810400 is about 774.6257784004.

Adding to 464810400 its reverse (4018464), we get a palindrome (468828864).

The spelling of 464810400 in words is "four hundred sixty-four million, eight hundred ten thousand, four hundred".