77928640398400 has 189 divisors, whose sum is σ = 210780509103493. Its totient is φ = 28336274982400.

The previous prime is 77928640398359. The next prime is 77928640398409. The reversal of 77928640398400 is 489304682977.

It is a happy number.

The square root of 77928640398400 is 8827720.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 28054310543424 + 49874329854976 = 5296632^2 + 7062176^2 .

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (77928640398409) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 3884186769 + ... + 3884206831.

Almost surely, 2^{77928640398400} is an apocalyptic number.

77928640398400 is the 8827720-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77928640398400

77928640398400 is an abundant number, since it is smaller than the sum of its proper divisors (132851868705093).

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

77928640398400 is an frugal number, since it uses more digits than its factorization.

77928640398400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 40170 (or 20081 counting only the distinct ones).

The product of its (nonzero) digits is 146313216, while the sum is 67.

The spelling of 77928640398400 in words is "seventy-seven trillion, nine hundred twenty-eight billion, six hundred forty million, three hundred ninety-eight thousand, four hundred".