412117372800 has 1920 divisors, whose sum is σ = 1904072417280. Its totient is φ = 85598208000.

The previous prime is 412117372759. The next prime is 412117372837. The reversal of 412117372800 is 8273711214.

412117372800 is a `hidden beast` number, since 412 + 1 + 173 + 72 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1920).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 956188585 + ... + 956189015.

It is an arithmetic number, because the mean of its divisors is an integer number (991704384).

Almost surely, 2^412117372800 is an apocalyptic number.

412117372800 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 412117372800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (952036208640).

412117372800 is an abundant number, since it is smaller than the sum of its proper divisors (1491955044480).

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

412117372800 is a wasteful number, since it uses less digits than its factorization.

412117372800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 522 (or 496 counting only the distinct ones).

The product of its (nonzero) digits is 18816, while the sum is 36.

The spelling of 412117372800 in words is "four hundred twelve billion, one hundred seventeen million, three hundred seventy-two thousand, eight hundred".