461527200 has 288 divisors, whose sum is σ = 1743638400. Its totient is φ = 117596160.

The previous prime is 461527153. The next prime is 461527207. The reversal of 461527200 is 2725164.

461527200 is a `hidden beast` number, since 4 + 615 + 27 + 20 + 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 not an unprimeable number, because it can be changed into a prime (461527207) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 496336 + ... + 497264.

It is an arithmetic number, because the mean of its divisors is an integer number (6054300).

Almost surely, 2^461527200 is an apocalyptic number.

461527200 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 461527200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (871819200).

461527200 is an abundant number, since it is smaller than the sum of its proper divisors (1282111200).

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

461527200 is a wasteful number, since it uses less digits than its factorization.

461527200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 981 (or 962 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The square root of 461527200 is about 21483.1841215403. The cubic root of 461527200 is about 772.7976042517.

The spelling of 461527200 in words is "four hundred sixty-one million, five hundred twenty-seven thousand, two hundred".