312134860800 has 1134 divisors, whose sum is σ = 1348862357388. Its totient is φ = 71345111040.

The previous prime is 312134860757. The next prime is 312134860813. The reversal of 312134860800 is 8068431213.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Jordan-Polya number, since it can be written as (8!)² ⋅ 4! ⋅ (2!)³.

312134860800 is a `hidden beast` number, since 3 + 1 + 2 + 1 + 3 + 48 + 608 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1134).

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

It is an unprimeable number.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 44590694397 + ... + 44590694403.

Almost surely, 2^312134860800 is an apocalyptic number.

312134860800 is a gapful number since it is divisible by the number (30) 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 312134860800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (674431178694).

312134860800 is an abundant number, since it is smaller than the sum of its proper divisors (1036727496588).

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

312134860800 is an frugal number, since it uses more digits than its factorization.

312134860800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 79 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

312134860800 divided by its product of nonzero digits (27648) gives a square (11289600 = 3360²).

The spelling of 312134860800 in words is "three hundred twelve billion, one hundred thirty-four million, eight hundred sixty thousand, eight hundred".