312828364800 has 864 divisors, whose sum is σ = 1288648146240. Its totient is φ = 71044300800.

The previous prime is 312828364787. The next prime is 312828364831. The reversal of 312828364800 is 8463828213.

312828364800 is a `hidden beast` number, since 3 + 1 + 282 + 8 + 364 + 8 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

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, 945100635 + ... + 945100965.

It is an arithmetic number, because the mean of its divisors is an integer number (1491490910).

Almost surely, 2^312828364800 is an apocalyptic number.

312828364800 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 312828364800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (644324073120).

312828364800 is an abundant number, since it is smaller than the sum of its proper divisors (975819781440).

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

312828364800 is a wasteful number, since it uses less digits than its factorization.

312828364800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 669 (or 641 counting only the distinct ones).

The product of its (nonzero) digits is 442368, while the sum is 45.

The spelling of 312828364800 in words is "three hundred twelve billion, eight hundred twenty-eight million, three hundred sixty-four thousand, eight hundred".