51085288800 has 432 divisors, whose sum is σ = 221712996960. Its totient is φ = 10778296320.

The previous prime is 51085288783. The next prime is 51085288831. The reversal of 51085288800 is 888258015.

51085288800 is a `hidden beast` number, since 510 + 8 + 52 + 8 + 8 + 80 + 0 = 666.

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

It is a congruent number.

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 71 ways as a sum of consecutive naturals, for example, 616216 + ... + 694184.

It is an arithmetic number, because the mean of its divisors is an integer number (513224530).

Almost surely, 2^51085288800 is an apocalyptic number.

51085288800 is a gapful number since it is divisible by the number (50) 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 51085288800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (110856498480).

51085288800 is an abundant number, since it is smaller than the sum of its proper divisors (170627708160).

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

51085288800 is a wasteful number, since it uses less digits than its factorization.

51085288800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 78015 (or 77999 counting only the distinct ones).

The product of its (nonzero) digits is 204800, while the sum is 45.

The spelling of 51085288800 in words is "fifty-one billion, eighty-five million, two hundred eighty-eight thousand, eight hundred".