132768 has 36 divisors (see below), whose sum is σ = 378378. Its totient is φ = 44160.

The previous prime is 132763. The next prime is 132817. The reversal of 132768 is 867231.

It can be written as a sum of positive squares in only one way, i.e., 121104 + 11664 = 348^2 + 108^2 .

It is a tau number, because it is divible by the number of its divisors (36).

It is a Smith number, since the sum of its digits (27) coincides with the sum of the digits of its prime factors.

It is a nialpdrome in base 9.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 132768.

It is not an unprimeable number, because it can be changed into a prime (132761) by changing a digit.

132768 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 58 + ... + 518.

2¹³²⁷⁶⁸ is an apocalyptic number.

132768 is a gapful number since it is divisible by the number (18) 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 132768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (189189).

132768 is an abundant number, since it is smaller than the sum of its proper divisors (245610).

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

132768 is a wasteful number, since it uses less digits than its factorization.

132768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 477 (or 466 counting only the distinct ones).

The product of its digits is 2016, while the sum is 27.

The square root of 132768 is about 364.3734348165. The cubic root of 132768 is about 51.0149898268.

Adding to 132768 its reverse (867231), we get a palindrome (999999).

It can be divided in two parts, 132 and 768, that added together give a square (900 = 30²).

The spelling of 132768 in words is "one hundred thirty-two thousand, seven hundred sixty-eight".