72864 has 72 divisors (see below), whose sum is σ = 235872. Its totient is φ = 21120.

The previous prime is 72859. The next prime is 72869. The reversal of 72864 is 46827.

72864 = T₁₂ + T₁₃ + ... + T₇₅.

It is an interprime number because it is at equal distance from previous prime (72859) and next prime (72869).

It is a tau number, because it is divible by the number of its divisors (72).

It is not an unprimeable number, because it can be changed into a prime (72869) by changing a digit.

72864 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 3157 + ... + 3179.

It is an arithmetic number, because the mean of its divisors is an integer number (3276).

2⁷²⁸⁶⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (117936).

72864 is an abundant number, since it is smaller than the sum of its proper divisors (163008).

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

72864 is a wasteful number, since it uses less digits than its factorization.

72864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 50 (or 39 counting only the distinct ones).

The product of its digits is 2688, while the sum is 27.

The square root of 72864 is about 269.9333251008. The cubic root of 72864 is about 41.7674219424.

The spelling of 72864 in words is "seventy-two thousand, eight hundred sixty-four".