2978164000800 has 720 divisors, whose sum is σ = 11174466663360. Its totient is φ = 771535964160.

The previous prime is 2978164000783. The next prime is 2978164000831. The reversal of 2978164000800 is 80004618792.

2978164000800 is a `hidden beast` number, since 2 + 97 + 81 + 6 + 400 + 0 + 80 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×2978164000800² (a number of 26 digits) contains 22 as substring.

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 119 ways as a sum of consecutive naturals, for example, 353738991 + ... + 353747409.

It is an arithmetic number, because the mean of its divisors is an integer number (15520092588).

Almost surely, 2^{2978164000800} is an apocalyptic number.

2978164000800 is a gapful number since it is divisible by the number (20) 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 2978164000800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5587233331680).

2978164000800 is an abundant number, since it is smaller than the sum of its proper divisors (8196302662560).

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

2978164000800 is a wasteful number, since it uses less digits than its factorization.

2978164000800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 8607 (or 8585 counting only the distinct ones).

The product of its (nonzero) digits is 193536, while the sum is 45.

The spelling of 2978164000800 in words is "two trillion, nine hundred seventy-eight billion, one hundred sixty-four million, eight hundred", and thus it is an aban number.