407920032 has 324 divisors, whose sum is σ = 1380367170. Its totient is φ = 114057216.

The previous prime is 407920027. The next prime is 407920033. The reversal of 407920032 is 230029704.

It can be written as a sum of positive squares in 9 ways, for example, as 37896336 + 370023696 = 6156^2 + 19236^2 .

It is a junction number, because it is equal to n+sod(n) for n = 407919978 and 407920005.

It is not an unprimeable number, because it can be changed into a prime (407920033) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 14066194 + ... + 14066222.

Almost surely, 2^407920032 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 407920032, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (690183585).

407920032 is an abundant number, since it is smaller than the sum of its proper divisors (972447138).

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

407920032 is a wasteful number, since it uses less digits than its factorization.

407920032 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 105 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 3024, while the sum is 27.

The square root of 407920032 is about 20197.0302767511. The cubic root of 407920032 is about 741.6374938714.

Adding to 407920032 its reverse (230029704), we get a palindrome (637949736).

The spelling of 407920032 in words is "four hundred seven million, nine hundred twenty thousand, thirty-two".