407164320 has 240 divisors, whose sum is σ = 1457212680. Its totient is φ = 107053056.

The previous prime is 407164313. The next prime is 407164333. The reversal of 407164320 is 23461704.

It can be written as a sum of positive squares in 4 ways, for example, as 247495824 + 159668496 = 15732^2 + 12636^2 .

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is an unprimeable number.

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 39 ways as a sum of consecutive naturals, for example, 1153264 + ... + 1153616.

Almost surely, 2^407164320 is an apocalyptic number.

407164320 is a gapful number since it is divisible by the number (40) 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 407164320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (728606340).

407164320 is an abundant number, since it is smaller than the sum of its proper divisors (1050048360).

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

407164320 is a wasteful number, since it uses less digits than its factorization.

407164320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 469 (or 452 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 27.

The square root of 407164320 is about 20178.3131108624. The cubic root of 407164320 is about 741.1792252799.

The spelling of 407164320 in words is "four hundred seven million, one hundred sixty-four thousand, three hundred twenty".