407712 has 48 divisors (see below), whose sum is σ = 1112832. Its totient is φ = 130560.

The previous prime is 407707. The next prime is 407713. The reversal of 407712 is 217704.

407712 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (48).

It is not an unprimeable number, because it can be changed into a prime (407713) by changing a digit.

407712 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 7 ways as a sum of consecutive naturals, for example, 2908 + ... + 3044.

It is an arithmetic number, because the mean of its divisors is an integer number (23184).

2⁴⁰⁷⁷¹² 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 407712, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (556416).

407712 is an abundant number, since it is smaller than the sum of its proper divisors (705120).

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

407712 is a wasteful number, since it uses less digits than its factorization.

407712 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 181 (or 173 counting only the distinct ones).

The product of its (nonzero) digits is 392, while the sum is 21.

The square root of 407712 is about 638.5232963644. The cubic root of 407712 is about 74.1511398433.

The spelling of 407712 in words is "four hundred seven thousand, seven hundred twelve", and thus it is an iban number.