12972 has 24 divisors (see below), whose sum is σ = 32256. Its totient is φ = 4048.

The previous prime is 12967. The next prime is 12973. The reversal of 12972 is 27921.

It is a happy number.

12972 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a hoax number, since the sum of its digits (21) coincides with the sum of the digits of its distinct prime factors.

It is a nialpdrome in base 12.

It is not an unprimeable number, because it can be changed into a prime (12973) 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 7 ways as a sum of consecutive naturals, for example, 253 + ... + 299.

It is an arithmetic number, because the mean of its divisors is an integer number (1344).

2¹²⁹⁷² is an apocalyptic number.

12972 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 12972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (16128).

12972 is an abundant number, since it is smaller than the sum of its proper divisors (19284).

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

12972 is a wasteful number, since it uses less digits than its factorization.

12972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 77 (or 75 counting only the distinct ones).

The product of its digits is 252, while the sum is 21.

The square root of 12972 is about 113.8946881992. The cubic root of 12972 is about 23.4964533655.

Subtracting from 12972 its product of digits (252), we obtain a triangular number (12720 = T₁₅₉).

It can be divided in two parts, 12 and 972, that multiplied together give a square (11664 = 108²).

The spelling of 12972 in words is "twelve thousand, nine hundred seventy-two".