464390400 has 324 divisors, whose sum is σ = 1641634512. Its totient is φ = 115568640.

The previous prime is 464390393. The next prime is 464390413. The reversal of 464390400 is 4093464.

It is a super-2 number, since 2×464390400² = 431316887224320000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 6931167 + ... + 6931233.

Almost surely, 2^464390400 is an apocalyptic number.

464390400 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 464390400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (820817256).

464390400 is an abundant number, since it is smaller than the sum of its proper divisors (1177244112).

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

464390400 is a wasteful number, since it uses less digits than its factorization.

464390400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 134 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 10368, while the sum is 30.

The square root of 464390400 is about 21549.7192557119. The cubic root of 464390400 is about 774.3923922937.

The spelling of 464390400 in words is "four hundred sixty-four million, three hundred ninety thousand, four hundred".