461289600 has 384 divisors, whose sum is σ = 1783368000. Its totient is φ = 116121600.

The previous prime is 461289599. The next prime is 461289607. The reversal of 461289600 is 6982164.

461289600 is a `hidden beast` number, since 46 + 1 + 2 + 8 + 9 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (384).

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 (461289607) 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, 1641460 + ... + 1641740.

Almost surely, 2^461289600 is an apocalyptic number.

461289600 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 461289600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (891684000).

461289600 is an abundant number, since it is smaller than the sum of its proper divisors (1322078400).

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

461289600 is a wasteful number, since it uses less digits than its factorization.

461289600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 333 (or 310 counting only the distinct ones).

The product of its (nonzero) digits is 20736, while the sum is 36.

The square root of 461289600 is about 21477.6535031181. The cubic root of 461289600 is about 772.6649661831.

The spelling of 461289600 in words is "four hundred sixty-one million, two hundred eighty-nine thousand, six hundred".