312999242400 has 864 divisors, whose sum is σ = 1215139069872. Its totient is φ = 75350016000.

The previous prime is 312999242377. The next prime is 312999242401. The reversal of 312999242400 is 4242999213.

312999242400 is a `hidden beast` number, since 31 + 2 + 99 + 92 + 42 + 400 = 666.

It can be written as a sum of positive squares in 24 ways, for example, as 2799256464 + 310199985936 = 52908^2 + 556956^2 .

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

It is not an unprimeable number, because it can be changed into a prime (312999242401) by changing a digit.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 1068256654 + ... + 1068256946.

Almost surely, 2^312999242400 is an apocalyptic number.

312999242400 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 312999242400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (607569534936).

312999242400 is an abundant number, since it is smaller than the sum of its proper divisors (902139827472).

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

312999242400 is a wasteful number, since it uses less digits than its factorization.

312999242400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 546 (or 530 counting only the distinct ones).

The product of its (nonzero) digits is 279936, while the sum is 45.

The spelling of 312999242400 in words is "three hundred twelve billion, nine hundred ninety-nine million, two hundred forty-two thousand, four hundred".