408072 has 48 divisors (see below), whose sum is σ = 1190160. Its totient is φ = 116256.

The previous prime is 408071. The next prime is 408077. The reversal of 408072 is 270804.

It is a happy number.

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

It is not an unprimeable number, because it can be changed into a prime (408071) 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, 1003 + ... + 1349.

It is an arithmetic number, because the mean of its divisors is an integer number (24795).

2⁴⁰⁸⁰⁷² is an apocalyptic number.

408072 is a gapful number since it is divisible by the number (42) 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 408072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (595080).

408072 is an abundant number, since it is smaller than the sum of its proper divisors (782088).

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

408072 is a wasteful number, since it uses less digits than its factorization.

408072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 370 (or 359 counting only the distinct ones).

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

The square root of 408072 is about 638.8051346068. The cubic root of 408072 is about 74.1729579873.

Adding to 408072 its reverse (270804), we get a palindrome (678876).

The spelling of 408072 in words is "four hundred eight thousand, seventy-two".