164772 has 36 divisors (see below), whose sum is σ = 436800. Its totient is φ = 52272.

The previous prime is 164771. The next prime is 164789. The reversal of 164772 is 277461.

164772 = 33³ + 34³ + ... + 36³.

It is a tau number, because it is divible by the number of its divisors (36).

It is an Ulam number.

It is not an unprimeable number, because it can be changed into a prime (164771) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 729 + ... + 927.

2¹⁶⁴⁷⁷² is an apocalyptic number.

164772 is a gapful number since it is divisible by the number (12) 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 164772, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (218400).

164772 is an abundant number, since it is smaller than the sum of its proper divisors (272028).

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

164772 is a wasteful number, since it uses less digits than its factorization.

164772 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 232 (or 227 counting only the distinct ones).

The product of its digits is 2352, while the sum is 27.

The square root of 164772 is about 405.9211746140. The cubic root of 164772 is about 54.8227905275.

The spelling of 164772 in words is "one hundred sixty-four thousand, seven hundred seventy-two".