461952400 has 300 divisors, whose sum is σ = 1432016852. Its totient is φ = 142248960.

The previous prime is 461952383. The next prime is 461952427. The reversal of 461952400 is 4259164.

It can be written as a sum of positive squares in 6 ways, for example, as 5531904 + 456420496 = 2352^2 + 21364^2 .

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 12485182 + ... + 12485218.

Almost surely, 2^461952400 is an apocalyptic number.

461952400 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 461952400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (716008426).

461952400 is an abundant number, since it is smaller than the sum of its proper divisors (970064452).

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

461952400 is a wasteful number, since it uses less digits than its factorization.

461952400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 96 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 8640, while the sum is 31.

The square root of 461952400 is about 21493.0779554721. The cubic root of 461952400 is about 773.0348547561.

The spelling of 461952400 in words is "four hundred sixty-one million, nine hundred fifty-two thousand, four hundred".