164409120 has 288 divisors, whose sum is σ = 603832320. Its totient is φ = 40642560.

The previous prime is 164409103. The next prime is 164409121. The reversal of 164409120 is 21904461.

164409120 is a `hidden beast` number, since 1 + 644 + 0 + 9 + 12 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-3 number, since 3×164409120³ (a number of 26 digits) contains 333 as substring.

It is not an unprimeable number, because it can be changed into a prime (164409121) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1294497 + ... + 1294623.

It is an arithmetic number, because the mean of its divisors is an integer number (2096640).

Almost surely, 2^164409120 is an apocalyptic number.

164409120 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 164409120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (301916160).

164409120 is an abundant number, since it is smaller than the sum of its proper divisors (439423200).

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

164409120 is a wasteful number, since it uses less digits than its factorization.

164409120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 208 (or 197 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 164409120 is about 12822.2119776581. The cubic root of 164409120 is about 547.8251524517.

The spelling of 164409120 in words is "one hundred sixty-four million, four hundred nine thousand, one hundred twenty".