171972 has 36 divisors (see below), whose sum is σ = 461916. Its totient is φ = 53760.

The previous prime is 171947. The next prime is 172001. The reversal of 171972 is 279171.

It can be written as a sum of positive squares in 2 ways, for example, as 125316 + 46656 = 354^2 + 216^2 .

It is a tau number, because it is divible by the number of its divisors (36).

It is an unprimeable number.

171972 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 11 ways as a sum of consecutive naturals, for example, 472 + ... + 752.

It is an arithmetic number, because the mean of its divisors is an integer number (12831).

2¹⁷¹⁹⁷² is an apocalyptic number.

171972 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 171972, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (230958).

171972 is an abundant number, since it is smaller than the sum of its proper divisors (289944).

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

171972 is a wasteful number, since it uses less digits than its factorization.

171972 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 308 (or 303 counting only the distinct ones).

The product of its digits is 882, while the sum is 27.

The square root of 171972 is about 414.6950686951. The cubic root of 171972 is about 55.6099597430.

The spelling of 171972 in words is "one hundred seventy-one thousand, nine hundred seventy-two".