312319378800 has 600 divisors, whose sum is σ = 1316868371280. Its totient is φ = 69888614400.

The previous prime is 312319378747. The next prime is 312319378823. The reversal of 312319378800 is 8873913213.

It is a happy number.

312319378800 is a `hidden beast` number, since 312 + 3 + 193 + 78 + 80 + 0 = 666.

312319378800 is digitally balanced in base 4, because in such base it contains all the possibile digits an equal number of times.

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

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

It is a congruent number.

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, 4599496 + ... + 4666904.

Almost surely, 2^312319378800 is an apocalyptic number.

312319378800 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 312319378800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (658434185640).

312319378800 is an abundant number, since it is smaller than the sum of its proper divisors (1004548992480).

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

312319378800 is a wasteful number, since it uses less digits than its factorization.

312319378800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 67463 (or 67443 counting only the distinct ones).

The product of its (nonzero) digits is 217728, while the sum is 45.

The spelling of 312319378800 in words is "three hundred twelve billion, three hundred nineteen million, three hundred seventy-eight thousand, eight hundred".