772096000 has 240 divisors, whose sum is σ = 2146893840. Its totient is φ = 275251200.

The previous prime is 772095991. The next prime is 772096019. The reversal of 772096000 is 690277.

It is a happy number.

It can be written as a sum of positive squares in 8 ways, for example, as 388562944 + 383533056 = 19712^2 + 19584^2 .

It is a super-2 number, since 2×772096000² = 1192264466432000000, which contains 22 as substring.

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 15 ways as a sum of consecutive naturals, for example, 26623986 + ... + 26624014.

It is an arithmetic number, because the mean of its divisors is an integer number (8945391).

Almost surely, 2^772096000 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 772096000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1073446920).

772096000 is an abundant number, since it is smaller than the sum of its proper divisors (1374797840).

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

772096000 is an equidigital number, since it uses as much as digits as its factorization.

772096000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 85 (or 49 counting only the distinct ones).

The product of its (nonzero) digits is 5292, while the sum is 31.

The square root of 772096000 is about 27786.6154829983. The cubic root of 772096000 is about 917.3965463320.

The spelling of 772096000 in words is "seven hundred seventy-two million, ninety-six thousand".