414468472320 has 1600 divisors, whose sum is σ = 1791791603712. Its totient is φ = 89579520000.

The previous prime is 414468472247. The next prime is 414468472321. The reversal of 414468472320 is 23274864414.

414468472320 is a `hidden beast` number, since 4 + 144 + 6 + 8 + 472 + 32 + 0 = 666.

It is a super-3 number, since 3×414468472320³ (a number of 36 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414468472321) by changing a digit.

It is a polite number, since it can be written in 159 ways as a sum of consecutive naturals, for example, 2744824245 + ... + 2744824395.

Almost surely, 2^414468472320 is an apocalyptic number.

414468472320 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 414468472320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (895895801856).

414468472320 is an abundant number, since it is smaller than the sum of its proper divisors (1377323131392).

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

414468472320 is a wasteful number, since it uses less digits than its factorization.

414468472320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 285 (or 260 counting only the distinct ones).

The product of its (nonzero) digits is 1032192, while the sum is 45.

The spelling of 414468472320 in words is "four hundred fourteen billion, four hundred sixty-eight million, four hundred seventy-two thousand, three hundred twenty".