464032000 has 144 divisors (see below), whose sum is σ = 1225394352. Its totient is φ = 174489600.

The previous prime is 464031989. The next prime is 464032039. The reversal of 464032000 is 230464.

It can be written as a sum of positive squares in 8 ways, for example, as 205979904 + 258052096 = 14352^2 + 16064^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 543574 + ... + 544426.

It is an arithmetic number, because the mean of its divisors is an integer number (8509683).

Almost surely, 2^464032000 is an apocalyptic number.

464032000 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 464032000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (612697176).

464032000 is an abundant number, since it is smaller than the sum of its proper divisors (761362352).

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

464032000 is an equidigital number, since it uses as much as digits as its factorization.

464032000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 901 (or 877 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 19.

The square root of 464032000 is about 21541.4019970846. The cubic root of 464032000 is about 774.1931248504.

Adding to 464032000 its reverse (230464), we get a palindrome (464262464).

It can be divided in two parts, 4 and 64032000, that added together give a square (64032004 = 8002²).

The spelling of 464032000 in words is "four hundred sixty-four million, thirty-two thousand".