17952 has 48 divisors (see below), whose sum is σ = 54432. Its totient is φ = 5120.

The previous prime is 17939. The next prime is 17957. The reversal of 17952 is 25971.

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

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 (17957) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 1048 + ... + 1064.

It is an arithmetic number, because the mean of its divisors is an integer number (1134).

2¹⁷⁹⁵² is an apocalyptic number.

17952 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 17952, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (27216).

17952 is an abundant number, since it is smaller than the sum of its proper divisors (36480).

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

17952 is a wasteful number, since it uses less digits than its factorization.

17952 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 41 (or 33 counting only the distinct ones).

The product of its digits is 630, while the sum is 24.

The square root of 17952 is about 133.9850737956. The cubic root of 17952 is about 26.1840977252.

It can be divided in two parts, 179 and 52, that added together give a triangular number (231 = T₂₁).

The spelling of 17952 in words is "seventeen thousand, nine hundred fifty-two".