135072 has 72 divisors (see below), whose sum is σ = 445536. Its totient is φ = 38016.

The previous prime is 135059. The next prime is 135077. The reversal of 135072 is 270531.

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

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nialpdrome in base 12.

It is not an unprimeable number, because it can be changed into a prime (135077) by changing a digit.

135072 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 (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1983 + ... + 2049.

It is an arithmetic number, because the mean of its divisors is an integer number (6188).

2¹³⁵⁰⁷² is an apocalyptic number.

135072 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 135072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (222768).

135072 is an abundant number, since it is smaller than the sum of its proper divisors (310464).

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

135072 is a wasteful number, since it uses less digits than its factorization.

135072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 90 (or 79 counting only the distinct ones).

The product of its (nonzero) digits is 210, while the sum is 18.

The square root of 135072 is about 367.5214279467. The cubic root of 135072 is about 51.3083966512.

The spelling of 135072 in words is "one hundred thirty-five thousand, seventy-two".