407972 has 12 divisors (see below), whose sum is σ = 738780. Its totient is φ = 196896.

The previous prime is 407971. The next prime is 407977. The reversal of 407972 is 279704.

It can be written as a sum of positive squares in 2 ways, for example, as 320356 + 87616 = 566^2 + 296^2 .

It is a hoax number, since the sum of its digits (29) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (29).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 407972.

It is not an unprimeable number, because it can be changed into a prime (407971) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1643 + ... + 1874.

It is an arithmetic number, because the mean of its divisors is an integer number (61565).

2⁴⁰⁷⁹⁷² is an apocalyptic number.

It is an amenable number.

407972 is a deficient number, since it is larger than the sum of its proper divisors (330808).

407972 is a wasteful number, since it uses less digits than its factorization.

407972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3550 (or 3548 counting only the distinct ones).

The product of its (nonzero) digits is 3528, while the sum is 29.

The square root of 407972 is about 638.7268586806. The cubic root of 407972 is about 74.1668986793.

The spelling of 407972 in words is "four hundred seven thousand, nine hundred seventy-two".