312145066800 has 1440 divisors, whose sum is σ = 1347545751552. Its totient is φ = 67905008640.

The previous prime is 312145066799. The next prime is 312145066801. The reversal of 312145066800 is 8660541213.

It is a happy number.

312145066800 is a `hidden beast` number, since 3 + 121 + 450 + 6 + 6 + 80 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (312145066799) and next prime (312145066801).

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

It is not an unprimeable number, because it can be changed into a prime (312145066801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 1375088287 + ... + 1375088513.

Almost surely, 2^312145066800 is an apocalyptic number.

312145066800 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 312145066800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (673772875776).

312145066800 is an abundant number, since it is smaller than the sum of its proper divisors (1035400684752).

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

312145066800 is a wasteful number, since it uses less digits than its factorization.

312145066800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 357 (or 334 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The spelling of 312145066800 in words is "three hundred twelve billion, one hundred forty-five million, sixty-six thousand, eight hundred".