78516345600 has 1620 divisors, whose sum is σ = 369720195768. Its totient is φ = 16257024000.

The previous prime is 78516345569. The next prime is 78516345601. The reversal of 78516345600 is 654361587.

78516345600 is a `hidden beast` number, since 7 + 8 + 5 + 1 + 6 + 34 + 5 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (1620).

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

It is not an unprimeable number, because it can be changed into a prime (78516345601) by changing a digit.

It is a polite number, since it can be written in 179 ways as a sum of consecutive naturals, for example, 279417460 + ... + 279417740.

Almost surely, 2^78516345600 is an apocalyptic number.

78516345600 is a gapful number since it is divisible by the number (70) 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 78516345600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (184860097884).

78516345600 is an abundant number, since it is smaller than the sum of its proper divisors (291203850168).

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

78516345600 is a wasteful number, since it uses less digits than its factorization.

78516345600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 344 (or 309 counting only the distinct ones).

The product of its (nonzero) digits is 604800, while the sum is 45.

The spelling of 78516345600 in words is "seventy-eight billion, five hundred sixteen million, three hundred forty-five thousand, six hundred".