464413824 has 288 divisors, whose sum is σ = 1606051200. Its totient is φ = 131010048.

The previous prime is 464413819. The next prime is 464413867. The reversal of 464413824 is 428314464.

464413824 is a `hidden beast` number, since 4 + 644 + 1 + 3 + 8 + 2 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a nude number because it is divisible by every one of its digits.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 5878617 + ... + 5878695.

Almost surely, 2^464413824 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 464413824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (803025600).

464413824 is an abundant number, since it is smaller than the sum of its proper divisors (1141637376).

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

464413824 is an frugal number, since it uses more digits than its factorization.

464413824 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 124 (or 91 counting only the distinct ones).

The product of its digits is 73728, while the sum is 36.

The square root of 464413824 is about 21550.2627362174. The cubic root of 464413824 is about 774.4054122746.

The spelling of 464413824 in words is "four hundred sixty-four million, four hundred thirteen thousand, eight hundred twenty-four".