461408400 has 360 divisors, whose sum is σ = 1712640384. Its totient is φ = 119232000.

The previous prime is 461408393. The next prime is 461408401. The reversal of 461408400 is 4804164.

461408400 is a `hidden beast` number, since 4 + 614 + 0 + 8 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (360).

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

It is not an unprimeable number, because it can be changed into a prime (461408401) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 4568350 + ... + 4568450.

Almost surely, 2^461408400 is an apocalyptic number.

461408400 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 461408400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (856320192).

461408400 is an abundant number, since it is smaller than the sum of its proper divisors (1251231984).

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

461408400 is a wasteful number, since it uses less digits than its factorization.

461408400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 181 (or 158 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 27.

The square root of 461408400 is about 21480.4189903270. The cubic root of 461408400 is about 772.7312909092.

The spelling of 461408400 in words is "four hundred sixty-one million, four hundred eight thousand, four hundred".