820551416400 has 360 divisors, whose sum is σ = 2974299459040. Its totient is φ = 217235934720.

The previous prime is 820551416371. The next prime is 820551416401. The reversal of 820551416400 is 4614155028.

It is a happy number.

820551416400 is a `hidden beast` number, since 8 + 2 + 0 + 5 + 5 + 1 + 4 + 1 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (360).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (820551416401) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 13480434 + ... + 13541166.

Almost surely, 2^820551416400 is an apocalyptic number.

820551416400 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 820551416400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1487149729520).

820551416400 is an abundant number, since it is smaller than the sum of its proper divisors (2153748042640).

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

820551416400 is a wasteful number, since it uses less digits than its factorization.

820551416400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 60905 (or 60882 counting only the distinct ones).

The product of its (nonzero) digits is 38400, while the sum is 36.

The spelling of 820551416400 in words is "eight hundred twenty billion, five hundred fifty-one million, four hundred sixteen thousand, four hundred".