461260800 has 864 divisors, whose sum is σ = 2217983040. Its totient is φ = 88473600.

The previous prime is 461260799. The next prime is 461260829. The reversal of 461260800 is 8062164.

461260800 is a `hidden beast` number, since 46 + 12 + 608 + 0 + 0 = 666.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 35481594 + ... + 35481606.

It is an arithmetic number, because the mean of its divisors is an integer number (2567110).

Almost surely, 2^461260800 is an apocalyptic number.

461260800 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 461260800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1108991520).

461260800 is an abundant number, since it is smaller than the sum of its proper divisors (1756722240).

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

461260800 is a wasteful number, since it uses less digits than its factorization.

461260800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 69 (or 41 counting only the distinct ones).

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

The square root of 461260800 is about 21476.9830283492. The cubic root of 461260800 is about 772.6488857468.

The spelling of 461260800 in words is "four hundred sixty-one million, two hundred sixty thousand, eight hundred".