415228320 has 288 divisors, whose sum is σ = 1566072144. Its totient is φ = 99532800.

The previous prime is 415228309. The next prime is 415228321. The reversal of 415228320 is 23822514.

415228320 is a `hidden beast` number, since 41 + 522 + 83 + 20 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 14107536 + 401120784 = 3756^2 + 20028^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415228321) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 767250 + ... + 767790.

Almost surely, 2^415228320 is an apocalyptic number.

415228320 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 415228320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (783036072).

415228320 is an abundant number, since it is smaller than the sum of its proper divisors (1150843824).

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

415228320 is a wasteful number, since it uses less digits than its factorization.

415228320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 616 (or 605 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

The square root of 415228320 is about 20377.1519109026. The cubic root of 415228320 is about 746.0403584411.

The spelling of 415228320 in words is "four hundred fifteen million, two hundred twenty-eight thousand, three hundred twenty".