2164838400 has 546 divisors, whose sum is σ = 8326069590. Its totient is φ = 557383680.

The previous prime is 2164838399. The next prime is 2164838419. The reversal of 2164838400 is 48384612.

2164838400 is a `hidden beast` number, since 2 + 1 + 648 + 3 + 8 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 146313216 + 2018525184 = 12096^2 + 44928^2 .

It is a super-2 number, since 2×2164838400² = 9373050596229120000, which contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 41 ways as a sum of consecutive naturals, for example, 74649586 + ... + 74649614.

Almost surely, 2^2164838400 is an apocalyptic number.

2164838400 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 2164838400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (4163034795).

2164838400 is an abundant number, since it is smaller than the sum of its proper divisors (6161231190).

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

2164838400 is an frugal number, since it uses more digits than its factorization.

2164838400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 81 (or 39 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 36.

The square root of 2164838400 is about 46527.8239336421. The cubic root of 2164838400 is about 1293.6252809830.

The spelling of 2164838400 in words is "two billion, one hundred sixty-four million, eight hundred thirty-eight thousand, four hundred".