128772 has 54 divisors (see below), whose sum is σ = 383838. Its totient is φ = 36288.

The previous prime is 128767. The next prime is 128813. The reversal of 128772 is 277821.

It can be written as a sum of positive squares in only one way, i.e., 112896 + 15876 = 336^2 + 126^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 1728 + ... + 1800.

2¹²⁸⁷⁷² is an apocalyptic number.

128772 is a gapful number since it is divisible by the number (12) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 128772, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (191919).

128772 is an abundant number, since it is smaller than the sum of its proper divisors (255066).

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

128772 is a wasteful number, since it uses less digits than its factorization.

128772 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 97 (or 85 counting only the distinct ones).

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

The square root of 128772 is about 358.8481573033. The cubic root of 128772 is about 50.4979576340.

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

The spelling of 128772 in words is "one hundred twenty-eight thousand, seven hundred seventy-two".