72408 has 32 divisors (see below), whose sum is σ = 207360. Its totient is φ = 20640.

The previous prime is 72383. The next prime is 72421. The reversal of 72408 is 80427.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a congruent number.

It is an unprimeable number.

72408 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 7 ways as a sum of consecutive naturals, for example, 48 + ... + 383.

It is an arithmetic number, because the mean of its divisors is an integer number (6480).

2⁷²⁴⁰⁸ 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 72408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (103680).

72408 is an abundant number, since it is smaller than the sum of its proper divisors (134952).

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

72408 is a wasteful number, since it uses less digits than its factorization.

72408 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 447 (or 443 counting only the distinct ones).

The product of its (nonzero) digits is 448, while the sum is 21.

The square root of 72408 is about 269.0873464138. The cubic root of 72408 is about 41.6801094403.

It can be divided in two parts, 7 and 2408, that added together give a triangular number (2415 = T₆₉).

The spelling of 72408 in words is "seventy-two thousand, four hundred eight".