2164735310400 has 756 divisors, whose sum is σ = 8802117183132. Its totient is φ = 501500805120.

The previous prime is 2164735310399. The next prime is 2164735310411. The reversal of 2164735310400 is 40135374612.

2164735310400 is a `hidden beast` number, since 2 + 1 + 647 + 3 + 5 + 3 + 1 + 0 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 18 ways, for example, as 1248243093504 + 916492216896 = 1117248^2 + 957336^2 .

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 54080794 + ... + 54120806.

It is an arithmetic number, because the mean of its divisors is an integer number (11643012147).

Almost surely, 2^{2164735310400} is an apocalyptic number.

2164735310400 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 2164735310400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4401058591566).

2164735310400 is an abundant number, since it is smaller than the sum of its proper divisors (6637381872732).

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

2164735310400 is a wasteful number, since it uses less digits than its factorization.

2164735310400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 40088 (or 40053 counting only the distinct ones).

The product of its (nonzero) digits is 60480, while the sum is 36.

The spelling of 2164735310400 in words is "two trillion, one hundred sixty-four billion, seven hundred thirty-five million, three hundred ten thousand, four hundred".