464640000 has 360 divisors, whose sum is σ = 1701439740. Its totient is φ = 112640000.

The previous prime is 464639957. The next prime is 464640013. The reversal of 464640000 is 46464.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 42239995 + ... + 42240005.

Almost surely, 2^464640000 is an apocalyptic number.

464640000 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 464640000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (850719870).

464640000 is an abundant number, since it is smaller than the sum of its proper divisors (1236799740).

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

464640000 is an equidigital number, since it uses as much as digits as its factorization.

464640000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 67 (or 21 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 24.

The square root of 464640000 is about 21555.5097364920. The cubic root of 464640000 is about 774.5311072786.

Multiplying 464640000 by its sum of digits (24), we get a square (11151360000 = 105600²).

464640000 divided by its sum of digits (24) gives a square (19360000 = 4400²).

Adding to 464640000 its reverse (46464), we get a palindrome (464686464).

Multiplying 464640000 by its reverse (46464), we get a square (21589032960000 = 4646400²).

464640000 divided by its reverse (46464) gives a 4-th power (10000 = 10⁴).

The spelling of 464640000 in words is "four hundred sixty-four million, six hundred forty thousand".