77852160400 has 135 divisors (see below), whose sum is σ = 217686153411. Its totient is φ = 26678776320.

The previous prime is 77852160343. The next prime is 77852160401. The reversal of 77852160400 is 406125877.

The square root of 77852160400 is 279020.

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

It can be written as a sum of positive squares in 4 ways, for example, as 763748496 + 77088411904 = 27636^2 + 277648^2 .

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 (77852160401) by changing a digit.

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 26 ways as a sum of consecutive naturals, for example, 39061804 + ... + 39063796.

Almost surely, 2^77852160400 is an apocalyptic number.

77852160400 is a gapful number since it is divisible by the number (70) formed by its first and last digit.

77852160400 is the 279020-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77852160400

77852160400 is an abundant number, since it is smaller than the sum of its proper divisors (139833993011).

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

77852160400 is an equidigital number, since it uses as much as digits as its factorization.

77852160400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4018 (or 2007 counting only the distinct ones).

The product of its (nonzero) digits is 94080, while the sum is 40.

The spelling of 77852160400 in words is "seventy-seven billion, eight hundred fifty-two million, one hundred sixty thousand, four hundred".