173952 has 48 divisors (see below), whose sum is σ = 503880. Its totient is φ = 57600.

The previous prime is 173933. The next prime is 173969. The reversal of 173952 is 259371.

It is a tau number, because it is divible by the number of its divisors (48).

It is a Smith number, since the sum of its digits (27) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is an unprimeable number.

173952 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 5 ways as a sum of consecutive naturals, for example, 1077 + ... + 1227.

173952 is a Friedman number, since it can be written as 1359*2^7, using all its digits and the basic arithmetic operations.

2¹⁷³⁹⁵² is an apocalyptic number.

173952 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 173952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (251940).

173952 is an abundant number, since it is smaller than the sum of its proper divisors (329928).

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

173952 is a wasteful number, since it uses less digits than its factorization.

173952 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 171 (or 156 counting only the distinct ones).

The product of its digits is 1890, while the sum is 27.

The square root of 173952 is about 417.0755327276. The cubic root of 173952 is about 55.8225676627.

It can be divided in two parts, 17 and 3952, that added together give a square (3969 = 63²).

The spelling of 173952 in words is "one hundred seventy-three thousand, nine hundred fifty-two".