462758400 has 480 divisors, whose sum is σ = 1846965120. Its totient is φ = 112803840.

The previous prime is 462758369. The next prime is 462758407. The reversal of 462758400 is 4857264.

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is not an unprimeable number, because it can be changed into a prime (462758407) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 4492749 + ... + 4492851.

It is an arithmetic number, because the mean of its divisors is an integer number (3847844).

Almost surely, 2^462758400 is an apocalyptic number.

462758400 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 462758400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (923482560).

462758400 is an abundant number, since it is smaller than the sum of its proper divisors (1384206720).

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

462758400 is a wasteful number, since it uses less digits than its factorization.

462758400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 153 (or 126 counting only the distinct ones).

The product of its (nonzero) digits is 53760, while the sum is 36.

The square root of 462758400 is about 21511.8200066847. The cubic root of 462758400 is about 773.4841824899.

The spelling of 462758400 in words is "four hundred sixty-two million, seven hundred fifty-eight thousand, four hundred".