772164000 has 288 divisors, whose sum is σ = 2782699920. Its totient is φ = 202752000.

The previous prime is 772163983. The next prime is 772164007. The reversal of 772164000 is 461277.

It can be written as a sum of positive squares in 8 ways, for example, as 16353936 + 755810064 = 4044^2 + 27492^2 .

It is a tau number, because it is divible by the number of its divisors (288).

It is not an unprimeable number, because it can be changed into a prime (772164007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 3203880 + ... + 3204120.

Almost surely, 2^772164000 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 772164000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1391349960).

772164000 is an abundant number, since it is smaller than the sum of its proper divisors (2010535920).

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

772164000 is a wasteful number, since it uses less digits than its factorization.

772164000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 361 (or 340 counting only the distinct ones).

The product of its (nonzero) digits is 2352, while the sum is 27.

The square root of 772164000 is about 27787.8390667572. The cubic root of 772164000 is about 917.4234778422.

The spelling of 772164000 in words is "seven hundred seventy-two million, one hundred sixty-four thousand".