213972 has 24 divisors (see below), whose sum is σ = 544992. Its totient is φ = 64800.

The previous prime is 213953. The next prime is 213973. The reversal of 213972 is 279312.

213972 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (213973) by changing a digit.

213972 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 679 + ... + 942.

It is an arithmetic number, because the mean of its divisors is an integer number (22708).

2²¹³⁹⁷² is an apocalyptic number.

213972 is a gapful number since it is divisible by the number (22) formed by its first and last digit.

It is an amenable number.

213972 is an abundant number, since it is smaller than the sum of its proper divisors (331020).

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

213972 is a wasteful number, since it uses less digits than its factorization.

213972 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1639 (or 1637 counting only the distinct ones).

The product of its digits is 756, while the sum is 24.

The square root of 213972 is about 462.5710756197. The cubic root of 213972 is about 59.8116314627.

It can be divided in two parts, 2139 and 72, that added together give a triangular number (2211 = T₆₆).

The spelling of 213972 in words is "two hundred thirteen thousand, nine hundred seventy-two".