77728896 has 336 divisors, whose sum is σ = 285961590. Its totient is φ = 20901888.

The previous prime is 77728877. The next prime is 77728909. The reversal of 77728896 is 69882777.

It can be written as a sum of positive squares in only one way, i.e., 57153600 + 20575296 = 7560^2 + 4536^2 .

It is a tau number, because it is divible by the number of its divisors (336).

It is a Smith number, since the sum of its digits (54) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a nude number because it is divisible by every one of its digits.

Its product of digits (2370816) is a multiple of the sum of its prime factors (63).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 41 ways as a sum of consecutive naturals, for example, 4572280 + ... + 4572296.

Almost surely, 2^77728896 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 77728896, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (142980795).

77728896 is an abundant number, since it is smaller than the sum of its proper divisors (208232694).

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

77728896 is an equidigital number, since it uses as much as digits as its factorization.

77728896 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 63 (or 29 counting only the distinct ones).

The product of its digits is 2370816, while the sum is 54.

The square root of 77728896 is about 8816.3992650061. The cubic root of 77728896 is about 426.7702786562.

The spelling of 77728896 in words is "seventy-seven million, seven hundred twenty-eight thousand, eight hundred ninety-six".