77729440000 has 405 divisors, whose sum is σ = 211103574451. Its totient is φ = 28549120000.

The previous prime is 77729439989. The next prime is 77729440003. The reversal of 77729440000 is 4492777.

The square root of 77729440000 is 278800.

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

It can be written as a sum of positive squares in 22 ways, for example, as 56324579584 + 21404860416 = 237328^2 + 146304^2 .

It is a Harshad number since it is a multiple of its sum of digits (40).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (77729440003) by changing a digit.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 1895839980 + ... + 1895840020.

Almost surely, 2^77729440000 is an apocalyptic number.

77729440000 is the 278800-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77729440000

77729440000 is an abundant number, since it is smaller than the sum of its proper divisors (133374134451).

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

77729440000 is an frugal number, since it uses more digits than its factorization.

77729440000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 152 (or 65 counting only the distinct ones).

The product of its (nonzero) digits is 98784, while the sum is 40.

The spelling of 77729440000 in words is "seventy-seven billion, seven hundred twenty-nine million, four hundred forty thousand".