413908500096000 has 5632 divisors, whose sum is σ = 1949837717667840. Its totient is φ = 84276412416000.

The previous prime is 413908500095777. The next prime is 413908500096019. The reversal of 413908500096000 is 690005809314.

It is a happy number.

413908500096000 is a `hidden beast` number, since 4 + 1 + 39 + 0 + 8 + 5 + 0 + 0 + 0 + 9 + 600 + 0 = 666.

It is a hoax number, since the sum of its digits (45) coincides with the sum of the digits of its distinct prime factors.

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 511 ways as a sum of consecutive naturals, for example, 1717462655880 + ... + 1717462656120.

It is an arithmetic number, because the mean of its divisors is an integer number (346206981120).

Almost surely, 2^{413908500096000} is an apocalyptic number.

413908500096000 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 413908500096000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (974918858833920).

413908500096000 is an abundant number, since it is smaller than the sum of its proper divisors (1535929217571840).

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

413908500096000 is a wasteful number, since it uses less digits than its factorization.

413908500096000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 475 (or 441 counting only the distinct ones).

The product of its (nonzero) digits is 233280, while the sum is 45.

The spelling of 413908500096000 in words is "four hundred thirteen trillion, nine hundred eight billion, five hundred million, ninety-six thousand".