17680 has 40 divisors (see below), whose sum is σ = 46872. Its totient is φ = 6144.

The previous prime is 17669. The next prime is 17681. The reversal of 17680 is 8671.

17680 is digitally balanced in base 6, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 4 ways, for example, as 1296 + 16384 = 36^2 + 128^2 .

It is a tau number, because it is divible by the number of its divisors (40).

17680 is an undulating number in base 13.

17680 is strictly pandigital in base 6.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (17681) 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, 1032 + ... + 1048.

2¹⁷⁶⁸⁰ is an apocalyptic number.

17680 is a gapful number since it is divisible by the number (10) 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 17680, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (23436).

17680 is an abundant number, since it is smaller than the sum of its proper divisors (29192).

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

17680 is a wasteful number, since it uses less digits than its factorization.

17680 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 43 (or 37 counting only the distinct ones).

The product of its (nonzero) digits is 336, while the sum is 22.

The square root of 17680 is about 132.9661611088. The cubic root of 17680 is about 26.0511812345.

Subtracting from 17680 its reverse (8671), we obtain a palindrome (9009).

It can be divided in two parts, 176 and 80, that added together give a 8-th power (256 = 2⁸).

The spelling of 17680 in words is "seventeen thousand, six hundred eighty".