135972 has 24 divisors (see below), whose sum is σ = 352800. Its totient is φ = 45288.

The previous prime is 135937. The next prime is 135977. The reversal of 135972 is 279531.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (135977) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 522 + ... + 737.

It is an arithmetic number, because the mean of its divisors is an integer number (14700).

135972 is a Friedman number, since it can be written as 9*(71^2-5)*3, using all its digits and the basic arithmetic operations.

2¹³⁵⁹⁷² is an apocalyptic number.

135972 is a gapful number since it is divisible by the number (12) formed by its first and last digit.

It is an amenable number.

135972 is an abundant number, since it is smaller than the sum of its proper divisors (216828).

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

135972 is a wasteful number, since it uses less digits than its factorization.

135972 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1272 (or 1264 counting only the distinct ones).

The product of its digits is 1890, while the sum is 27.

The square root of 135972 is about 368.7438135074. The cubic root of 135972 is about 51.4221023609.

It can be divided in two parts, 1359 and 72, that added together give a triangular number (1431 = T₅₃).

The spelling of 135972 in words is "one hundred thirty-five thousand, nine hundred seventy-two".