83406855456000 has 864 divisors, whose sum is σ = 311045980845600. Its totient is φ = 21435118387200.

The previous prime is 83406855455923. The next prime is 83406855456047. The reversal of 83406855456000 is 65455860438.

83406855456000 is a `hidden beast` number, since 8 + 34 + 0 + 6 + 8 + 5 + 545 + 60 + 0 + 0 = 666.

It can be written as a sum of positive squares in 16 ways, for example, as 72585492562944 + 10821362893056 = 8519712^2 + 3289584^2 .

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 4652055036 + ... + 4652072964.

It is an arithmetic number, because the mean of its divisors is an integer number (360006922275).

Almost surely, 2^{83406855456000} is an apocalyptic number.

83406855456000 is a gapful number since it is divisible by the number (80) 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 83406855456000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (155522990422800).

83406855456000 is an abundant number, since it is smaller than the sum of its proper divisors (227639125389600).

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

83406855456000 is a wasteful number, since it uses less digits than its factorization.

83406855456000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 18552 (or 18525 counting only the distinct ones).

The product of its (nonzero) digits is 13824000, while the sum is 54.

The spelling of 83406855456000 in words is "eighty-three trillion, four hundred six billion, eight hundred fifty-five million, four hundred fifty-six thousand".