164438400 has 192 divisors, whose sum is σ = 619246080. Its totient is φ = 37570560.

The previous prime is 164438389. The next prime is 164438423. The reversal of 164438400 is 4834461.

It is a tau number, because it is divible by the number of its divisors (192).

It is a super-3 number, since 3×164438400³ (a number of 26 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 65977 + ... + 68423.

It is an arithmetic number, because the mean of its divisors is an integer number (3225240).

Almost surely, 2^164438400 is an apocalyptic number.

164438400 is a gapful number since it is divisible by the number (10) 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 164438400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (309623040).

164438400 is an abundant number, since it is smaller than the sum of its proper divisors (454807680).

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

164438400 is a wasteful number, since it uses less digits than its factorization.

164438400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2481 (or 2464 counting only the distinct ones).

The product of its (nonzero) digits is 9216, while the sum is 30.

The square root of 164438400 is about 12823.3536955042. The cubic root of 164438400 is about 547.8576716703.

The spelling of 164438400 in words is "one hundred sixty-four million, four hundred thirty-eight thousand, four hundred".