463814400 has 648 divisors, whose sum is σ = 1950343920. Its totient is φ = 96337920.

The previous prime is 463814363. The next prime is 463814413. The reversal of 463814400 is 4418364.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 15993586 + ... + 15993614.

It is an arithmetic number, because the mean of its divisors is an integer number (3009790).

Almost surely, 2^463814400 is an apocalyptic number.

463814400 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 463814400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (975171960).

463814400 is an abundant number, since it is smaller than the sum of its proper divisors (1486529520).

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

463814400 is a wasteful number, since it uses less digits than its factorization.

463814400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 89 (or 63 counting only the distinct ones).

The product of its (nonzero) digits is 9216, while the sum is 30.

The square root of 463814400 is about 21536.3506657929. The cubic root of 463814400 is about 774.0720909823.

The spelling of 463814400 in words is "four hundred sixty-three million, eight hundred fourteen thousand, four hundred".