820414656000 has 960 divisors, whose sum is σ = 3111766834176. Its totient is φ = 215405568000.

The previous prime is 820414655987. The next prime is 820414656011. The reversal of 820414656000 is 656414028.

820414656000 is a `hidden beast` number, since 8 + 2 + 0 + 4 + 1 + 46 + 5 + 600 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (960).

It is a Harshad number since it is a multiple of its sum of digits (36).

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, 1104191629 + ... + 1104192371.

Almost surely, 2^820414656000 is an apocalyptic number.

820414656000 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 820414656000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1555883417088).

820414656000 is an abundant number, since it is smaller than the sum of its proper divisors (2291352178176).

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

820414656000 is an frugal number, since it uses more digits than its factorization.

820414656000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 862 (or 824 counting only the distinct ones).

The product of its (nonzero) digits is 46080, while the sum is 36.

The spelling of 820414656000 in words is "eight hundred twenty billion, four hundred fourteen million, six hundred fifty-six thousand".