416402085775104 has 3456 divisors, whose sum is σ = 1604172430586880. Its totient is φ = 104660729856000.

The previous prime is 416402085775079. The next prime is 416402085775177. The reversal of 416402085775104 is 401577580204614.

It is a happy number.

416402085775104 is a `hidden beast` number, since 4 + 1 + 6 + 40 + 2 + 0 + 85 + 7 + 7 + 510 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (3456).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 1727809484424 + ... + 1727809484664.

It is an arithmetic number, because the mean of its divisors is an integer number (464170263480).

Almost surely, 2^{416402085775104} is an apocalyptic number.

416402085775104 is a gapful number since it is divisible by the number (44) 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 416402085775104, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (802086215293440).

416402085775104 is an abundant number, since it is smaller than the sum of its proper divisors (1187770344811776).

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

416402085775104 is a wasteful number, since it uses less digits than its factorization.

416402085775104 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 476 (or 425 counting only the distinct ones).

The product of its (nonzero) digits is 7526400, while the sum is 54.

The spelling of 416402085775104 in words is "four hundred sixteen trillion, four hundred two billion, eighty-five million, seven hundred seventy-five thousand, one hundred four".