27972 has 48 divisors (see below), whose sum is σ = 85120. Its totient is φ = 7776.

The previous prime is 27967. The next prime is 27983.

27972 is nontrivially palindromic in base 10.

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

It is a nude number because it is divisible by every one of its digits.

Its product of digits (1764) is a multiple of the sum of its prime divisors (49).

It is a nialpdrome in base 6.

It is a zygodrome in base 6.

It is a congruent number.

It is an unprimeable 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 15 ways as a sum of consecutive naturals, for example, 738 + ... + 774.

2²⁷⁹⁷² is an apocalyptic number.

27972 is the 84-th decagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 27972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (42560).

27972 is an abundant number, since it is smaller than the sum of its proper divisors (57148).

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

27972 is a wasteful number, since it uses less digits than its factorization.

27972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 57 (or 49 counting only the distinct ones).

The product of its digits is 1764, while the sum is 27.

The square root of 27972 is about 167.2483183772. The cubic root of 27972 is about 30.3557643797.

It can be divided in two parts, 279 and 72, that added together give a triangular number (351 = T₂₆).

The spelling of 27972 in words is "twenty-seven thousand, nine hundred seventy-two".