172872 has 60 divisors (see below), whose sum is σ = 546195. Its totient is φ = 49392.

The previous prime is 172871. The next prime is 172877. The reversal of 172872 is 278271.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in only one way, i.e., 86436 + 86436 = 294^2 + 294^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=294.

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

It is an Ulam number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 172872.

It is not an unprimeable number, because it can be changed into a prime (172871) by changing a digit.

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 14 ways as a sum of consecutive naturals, for example, 24693 + ... + 24699.

172872 is a Friedman number, since it can be written as 8*(7*7*(2+1))^2, using all its digits and the basic arithmetic operations.

2¹⁷²⁸⁷² is an apocalyptic number.

172872 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 172872

172872 is an abundant number, since it is smaller than the sum of its proper divisors (373323).

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

172872 is an equidigital number, since it uses as much as digits as its factorization.

172872 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 40 (or 12 counting only the distinct ones).

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

The square root of 172872 is about 415.7787873377. The cubic root of 172872 is about 55.7068009105.

Multiplying 172872 by its product of digits (1568), we get a square (271063296 = 16464²).

The spelling of 172872 in words is "one hundred seventy-two thousand, eight hundred seventy-two".