217872 has 60 divisors (see below), whose sum is σ = 652860. Its totient is φ = 67584.

The previous prime is 217859. The next prime is 217901. The reversal of 217872 is 278712.

It can be written as a sum of positive squares in 2 ways, for example, as 104976 + 112896 = 324^2 + 336^2 .

It is a nialpdrome in base 12.

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 11 ways as a sum of consecutive naturals, for example, 2404 + ... + 2492.

It is an arithmetic number, because the mean of its divisors is an integer number (10881).

2²¹⁷⁸⁷² is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 217872, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (326430).

217872 is an abundant number, since it is smaller than the sum of its proper divisors (434988).

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

217872 is a wasteful number, since it uses less digits than its factorization.

217872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 120 (or 111 counting only the distinct ones).

The product of its digits is 1568, while the sum is 27.

The square root of 217872 is about 466.7676081306. The cubic root of 217872 is about 60.1728349897.

It can be divided in two parts, 2178 and 72, that multiplied together give a square (156816 = 396²).

The spelling of 217872 in words is "two hundred seventeen thousand, eight hundred seventy-two".