172752 has 40 divisors (see below), whose sum is σ = 461280. Its totient is φ = 55680.

The previous prime is 172751. The next prime is 172759. The reversal of 172752 is 257271.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (172751) 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 7 ways as a sum of consecutive naturals, for example, 2802 + ... + 2862.

It is an arithmetic number, because the mean of its divisors is an integer number (11532).

2¹⁷²⁷⁵² is an apocalyptic number.

172752 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 172752, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (230640).

172752 is an abundant number, since it is smaller than the sum of its proper divisors (288528).

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

172752 is a wasteful number, since it uses less digits than its factorization.

172752 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 131 (or 125 counting only the distinct ones).

The product of its digits is 980, while the sum is 24.

The square root of 172752 is about 415.6344547797. The cubic root of 172752 is about 55.6939082048.

The spelling of 172752 in words is "one hundred seventy-two thousand, seven hundred fifty-two".