172864 has 28 divisors (see below), whose sum is σ = 357124. Its totient is φ = 82944.

The previous prime is 172859. The next prime is 172867. The reversal of 172864 is 468271.

It can be written as a sum of positive squares in 2 ways, for example, as 129600 + 43264 = 360^2 + 208^2 .

Its product of digits (2688) is a multiple of the sum of its prime divisors (112).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (172867) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2332 + ... + 2404.

172864 is a Friedman number, since it can be written as 12*7^4*6-8, using all its digits and the basic arithmetic operations.

2¹⁷²⁸⁶⁴ 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 172864, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (178562).

172864 is an abundant number, since it is smaller than the sum of its proper divisors (184260).

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

172864 is an equidigital number, since it uses as much as digits as its factorization.

172864 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 122 (or 112 counting only the distinct ones).

The product of its digits is 2688, while the sum is 28.

The square root of 172864 is about 415.7691667260. The cubic root of 172864 is about 55.7059415825.

It can be divided in two parts, 1728 and 64, that multiplied together give a cube (110592 = 48³).

The spelling of 172864 in words is "one hundred seventy-two thousand, eight hundred sixty-four".