51657513868800 has 2400 divisors, whose sum is σ = 232440755196672. Its totient is φ = 11106427207680.

The previous prime is 51657513868781. The next prime is 51657513868801. The reversal of 51657513868800 is 886831575615.

51657513868800 is a `hidden beast` number, since 5 + 1 + 6 + 57 + 513 + 8 + 68 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (2400).

It is a super-2 number, since 2×51657513868800² (a number of 28 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (51657513868801) by changing a digit.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 29981144739 + ... + 29981146461.

Almost surely, 2^{51657513868800} is an apocalyptic number.

51657513868800 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 51657513868800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (116220377598336).

51657513868800 is an abundant number, since it is smaller than the sum of its proper divisors (180783241327872).

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

51657513868800 is an frugal number, since it uses more digits than its factorization.

51657513868800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1802 (or 1757 counting only the distinct ones).

The product of its (nonzero) digits is 48384000, while the sum is 63.

The spelling of 51657513868800 in words is "fifty-one trillion, six hundred fifty-seven billion, five hundred thirteen million, eight hundred sixty-eight thousand, eight hundred".