461975992045200 has 600 divisors, whose sum is σ = 1755968874180840. Its totient is φ = 115917524582400.

The previous prime is 461975992045193. The next prime is 461975992045229. The reversal of 461975992045200 is 2540299579164.

461975992045200 is a `hidden beast` number, since 4 + 6 + 1 + 9 + 75 + 99 + 20 + 452 + 0 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 113436814051584 + 348539177993616 = 10650672^2 + 18669204^2 .

It is a tau number, because it is divible by the number of its divisors (600).

It is a super-2 number, since 2×461975992045200² (a number of 30 digits) contains 22 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 2214662506 + ... + 2214871094.

Almost surely, 2^{461975992045200} is an apocalyptic number.

461975992045200 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 461975992045200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (877984437090420).

461975992045200 is an abundant number, since it is smaller than the sum of its proper divisors (1293992882135640).

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

461975992045200 is a wasteful number, since it uses less digits than its factorization.

461975992045200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 212657 (or 212637 counting only the distinct ones).

The product of its (nonzero) digits is 48988800, while the sum is 63.

The spelling of 461975992045200 in words is "four hundred sixty-one trillion, nine hundred seventy-five billion, nine hundred ninety-two million, forty-five thousand, two hundred".