172032 has 56 divisors (see below), whose sum is σ = 524256. Its totient is φ = 49152.

The previous prime is 172031. The next prime is 172049. The reversal of 172032 is 230271.

172032 divided by its product of nonzero digits (84) gives a 11-th power (2048 = 2^{11}).

It can be divided in two parts, 17203 and 2, that added together give a triangular number (17205 = T_{185}).

It is a tau number, because it is divible by the number of its divisors (56).

It is a nialpdrome in base 4 and base 8.

It is a zygodrome in base 4.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 172032.

It is not an unprimeable number, because it can be changed into a prime (172031) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 24573 + ... + 24579.

2^{172032} is an apocalyptic number.

172032 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 172032, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (262128).

172032 is an abundant number, since it is smaller than the sum of its proper divisors (352224).

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

172032 is an frugal number, since it uses more digits than its factorization.

172032 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 36 (or 12 counting only the distinct ones).

The product of its (nonzero) digits is 84, while the sum is 15.

The square root of 172032 is about 414.7674046981. The cubic root of 172032 is about 55.6164263182.

The spelling of 172032 in words is "one hundred seventy-two thousand, thirty-two".

Divisors: 1 2 3 4 6 7 8 12 14 16 21 24 28 32 42 48 56 64 84 96 112 128 168 192 224 256 336 384 448 512 672 768 896 1024 1344 1536 1792 2048 2688 3072 3584 4096 5376 6144 7168 8192 10752 12288 14336 21504 24576 28672 43008 57344 86016 172032

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