416003328000 has 2304 divisors, whose sum is σ = 1841641401600. Its totient is φ = 89181388800.

The previous prime is 416003327897. The next prime is 416003328007. The reversal of 416003328000 is 823300614.

It is a happy number.

416003328000 is a `hidden beast` number, since 4 + 1 + 600 + 33 + 28 + 0 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2304).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (416003328007) by changing a digit.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 9674495979 + ... + 9674496021.

It is an arithmetic number, because the mean of its divisors is an integer number (799323525).

Almost surely, 2^416003328000 is an apocalyptic number.

416003328000 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 416003328000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (920820700800).

416003328000 is an abundant number, since it is smaller than the sum of its proper divisors (1425638073600).

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

416003328000 is a wasteful number, since it uses less digits than its factorization.

416003328000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 135 (or 102 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 27.

Adding to 416003328000 its reverse (823300614), we get a palindrome (416826628614).

The spelling of 416003328000 in words is "four hundred sixteen billion, three million, three hundred twenty-eight thousand".