82758312489600 has 3456 divisors, whose sum is σ = 359321995581120. Its totient is φ = 18611041075200.

The previous prime is 82758312489551. The next prime is 82758312489613. The reversal of 82758312489600 is 698421385728.

82758312489600 is a `hidden beast` number, since 8 + 2 + 7 + 5 + 8 + 3 + 12 + 4 + 8 + 9 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (3456).

It is a super-2 number, since 2×82758312489600² (a number of 29 digits) contains 22 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 431 ways as a sum of consecutive naturals, for example, 420092956702 + ... + 420092956898.

It is a 1-persistent number, because it is pandigital, but 2⋅82758312489600 = 165516624979200 is not.

Almost surely, 2^{82758312489600} is an apocalyptic number.

82758312489600 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 82758312489600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (179660997790560).

82758312489600 is an abundant number, since it is smaller than the sum of its proper divisors (276563683091520).

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

82758312489600 is a wasteful number, since it uses less digits than its factorization.

82758312489600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 380 (or 342 counting only the distinct ones).

The product of its (nonzero) digits is 46448640, while the sum is 63.

The spelling of 82758312489600 in words is "eighty-two trillion, seven hundred fifty-eight billion, three hundred twelve million, four hundred eighty-nine thousand, six hundred".