164414030400 has 567 divisors, whose sum is σ = 609415391403. Its totient is φ = 42040166400.

The previous prime is 164414030329. The next prime is 164414030447. The reversal of 164414030400 is 4030414461.

The square root of 164414030400 is 405480.

It is a perfect power (a square), and thus also a powerful number.

164414030400 is a `hidden beast` number, since 1 + 644 + 14 + 0 + 3 + 0 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 602800704 + 163811229696 = 24552^2 + 404736^2 .

It is a super-3 number, since 3×164414030400³ (a number of 35 digits) contains 333 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 1508385546 + ... + 1508385654.

Almost surely, 2^164414030400 is an apocalyptic number.

164414030400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

164414030400 is the 405480-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 164414030400

164414030400 is an abundant number, since it is smaller than the sum of its proper divisors (445001361003).

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

164414030400 is a wasteful number, since it uses less digits than its factorization.

164414030400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 308 (or 150 counting only the distinct ones).

The product of its (nonzero) digits is 4608, while the sum is 27.

Adding to 164414030400 its reverse (4030414461), we get a palindrome (168444444861).

The spelling of 164414030400 in words is "one hundred sixty-four billion, four hundred fourteen million, thirty thousand, four hundred".