464400 has 120 divisors (see below), whose sum is σ = 1691360. Its totient is φ = 120960.

The previous prime is 464383. The next prime is 464413. The reversal of 464400 is 4464.

464400 = T₆₄ + T₆₅ + ... + T₁₄₄.

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

464400 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 10779 + ... + 10821.

2⁴⁶⁴⁴⁰⁰ is an apocalyptic number.

464400 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 464400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (845680).

464400 is an abundant number, since it is smaller than the sum of its proper divisors (1226960).

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

464400 is a wasteful number, since it uses less digits than its factorization.

464400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 70 (or 53 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 18.

The square root of 464400 is about 681.4690014960. The cubic root of 464400 is about 77.4397728404.

Adding to 464400 its reverse (4464), we get a palindrome (468864).

The spelling of 464400 in words is "four hundred sixty-four thousand, four hundred".