51405727017600 has 576 divisors, whose sum is σ = 186843602907000. Its totient is φ = 13455141765120.

The previous prime is 51405727017599. The next prime is 51405727017641. The reversal of 51405727017600 is 671072750415.

51405727017600 is a `hidden beast` number, since 5 + 1 + 4 + 0 + 5 + 7 + 27 + 0 + 17 + 600 = 666.

51405727017600 is digitally balanced in base 6, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 12 ways, for example, as 1319759820864 + 50085967196736 = 1148808^2 + 7077144^2 .

It is a tau number, because it is divible by the number of its divisors (576).

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 351085206 + ... + 351231594.

Almost surely, 2^{51405727017600} is an apocalyptic number.

51405727017600 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 51405727017600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (93421801453500).

51405727017600 is an abundant number, since it is smaller than the sum of its proper divisors (135437875889400).

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

51405727017600 is a wasteful number, since it uses less digits than its factorization.

51405727017600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 146645 (or 146625 counting only the distinct ones).

The product of its (nonzero) digits is 411600, while the sum is 45.

The spelling of 51405727017600 in words is "fifty-one trillion, four hundred five billion, seven hundred twenty-seven million, seventeen thousand, six hundred".