461138400 has 288 divisors, whose sum is σ = 1715827680. Its totient is φ = 119439360.

The previous prime is 461138399. The next prime is 461138443. The reversal of 461138400 is 4831164.

461138400 is a `hidden beast` number, since 4 + 611 + 3 + 8 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 798912 + ... + 799488.

It is an arithmetic number, because the mean of its divisors is an integer number (5957735).

Almost surely, 2^461138400 is an apocalyptic number.

461138400 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 461138400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (857913840).

461138400 is an abundant number, since it is smaller than the sum of its proper divisors (1254689280).

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

461138400 is a wasteful number, since it uses less digits than its factorization.

461138400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 643 (or 624 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 461138400 is about 21474.1332770382. The cubic root of 461138400 is about 772.5805364239.

Adding to 461138400 its reverse (4831164), we get a palindrome (465969564).

The spelling of 461138400 in words is "four hundred sixty-one million, one hundred thirty-eight thousand, four hundred".