77564390400 has 2112 divisors, whose sum is σ = 368436418560. Its totient is φ = 15571353600.

The previous prime is 77564390399. The next prime is 77564390429. The reversal of 77564390400 is 409346577.

77564390400 is a `hidden beast` number, since 77 + 56 + 43 + 90 + 400 = 666.

It is a super-2 number, since 2×77564390400² (a number of 23 digits) contains 22 as substring.

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 (13) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 1891814380 + ... + 1891814420.

Almost surely, 2^77564390400 is an apocalyptic number.

77564390400 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 77564390400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (184218209280).

77564390400 is an abundant number, since it is smaller than the sum of its proper divisors (290872028160).

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

77564390400 is a wasteful number, since it uses less digits than its factorization.

77564390400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 127 (or 98 counting only the distinct ones).

The product of its (nonzero) digits is 635040, while the sum is 45.

The spelling of 77564390400 in words is "seventy-seven billion, five hundred sixty-four million, three hundred ninety thousand, four hundred".