172224 has 84 divisors (see below), whose sum is σ = 554736. Its totient is φ = 50688.

The previous prime is 172223. The next prime is 172243. The reversal of 172224 is 422271.

172224 = T₃₉ + T₄₀ + ... + T₁₀₂.

It is a Cunningham number, because it is equal to 415²-1.

It is a super-2 number, since 2×172224² = 59322212352, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a junction number, because it is equal to n+sod(n) for n = 172197 and 172206.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (172223) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 7477 + ... + 7499.

It is an arithmetic number, because the mean of its divisors is an integer number (6604).

172224 is a Friedman number, since it can be written as (422-7)^2-1, using all its digits and the basic arithmetic operations.

2¹⁷²²²⁴ 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 172224, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (277368).

172224 is an abundant number, since it is smaller than the sum of its proper divisors (382512).

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

172224 is a wasteful number, since it uses less digits than its factorization.

172224 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 54 (or 41 counting only the distinct ones).

The product of its digits is 224, while the sum is 18.

The square root of 172224 is about 414.9987951790. The cubic root of 172224 is about 55.6371092603.

Adding to 172224 its reverse (422271), we get a palindrome (594495).

Subtracting 172224 from its reverse (422271), we obtain a cube (250047 = 63³).

It can be divided in two parts, 1722 and 24, that multiplied together give a triangular number (41328 = T₂₈₇).

The spelling of 172224 in words is "one hundred seventy-two thousand, two hundred twenty-four", and thus it is an iban number.