72456 has 16 divisors (see below), whose sum is σ = 181200. Its totient is φ = 24144.

The previous prime is 72431. The next prime is 72461. The reversal of 72456 is 65427.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (24), and also a Moran number because the ratio is a prime number: 3019 = 72456 / (7 + 2 + 4 + 5 + 6).

It is an unprimeable number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1486 + ... + 1533.

It is an arithmetic number, because the mean of its divisors is an integer number (11325).

2⁷²⁴⁵⁶ is an apocalyptic number.

It is an amenable number.

72456 is an abundant number, since it is smaller than the sum of its proper divisors (108744).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (90600).

72456 is a wasteful number, since it uses less digits than its factorization.

72456 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3028 (or 3024 counting only the distinct ones).

The product of its digits is 1680, while the sum is 24.

The square root of 72456 is about 269.1765220074. The cubic root of 72456 is about 41.6893174621.

It can be divided in two parts, 724 and 56, that added together give a triangular number (780 = T₃₉).

The spelling of 72456 in words is "seventy-two thousand, four hundred fifty-six".