772128 has 72 divisors (see below), whose sum is σ = 2515968. Its totient is φ = 220032.

The previous prime is 772127. The next prime is 772139. The reversal of 772128 is 821277.

It is a tau number, because it is divible by the number of its divisors (72).

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

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 772128.

It is not an unprimeable number, because it can be changed into a prime (772127) by changing a digit.

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 11 ways as a sum of consecutive naturals, for example, 1825 + ... + 2207.

It is an arithmetic number, because the mean of its divisors is an integer number (34944).

2⁷⁷²¹²⁸ 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 772128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1257984).

772128 is an abundant number, since it is smaller than the sum of its proper divisors (1743840).

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

772128 is a wasteful number, since it uses less digits than its factorization.

772128 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 406 (or 395 counting only the distinct ones).

The product of its digits is 1568, while the sum is 27.

The square root of 772128 is about 878.7081426731. The cubic root of 772128 is about 91.7409220181.

It can be divided in two parts, 772 and 128, that added together give a square (900 = 30²).

The spelling of 772128 in words is "seven hundred seventy-two thousand, one hundred twenty-eight".