312354560048400 has 300 divisors, whose sum is σ = 1123512196504500. Its totient is φ = 83109034229760.

The previous prime is 312354560048389. The next prime is 312354560048423. The reversal of 312354560048400 is 4840065453213.

312354560048400 is a `hidden beast` number, since 3 + 1 + 2 + 3 + 5 + 4 + 560 + 0 + 4 + 84 + 0 + 0 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 45927918864 + 312308632129536 = 214308^2 + 17672256^2 .

It is a tau number, because it is divible by the number of its divisors (300).

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 59 ways as a sum of consecutive naturals, for example, 3811996 + ... + 25283204.

It is an arithmetic number, because the mean of its divisors is an integer number (3745040655015).

Almost surely, 2^{312354560048400} is an apocalyptic number.

312354560048400 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 312354560048400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (561756098252250).

312354560048400 is an abundant number, since it is smaller than the sum of its proper divisors (811157636456100).

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

312354560048400 is a wasteful number, since it uses less digits than its factorization.

312354560048400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 21471688 (or 21471668 counting only the distinct ones).

The product of its (nonzero) digits is 1382400, while the sum is 45.

The spelling of 312354560048400 in words is "three hundred twelve trillion, three hundred fifty-four billion, five hundred sixty million, forty-eight thousand, four hundred".