17820 has 60 divisors (see below), whose sum is σ = 60984. Its totient is φ = 4320.
The previous prime is 17807. The next prime is 17827. The reversal of 17820 is 2871.
It is a tau number, because it is divible by the number of its divisors (60).
It is a Harshad number since it is a multiple of its sum of digits (18).
It is a plaindrome in base 14 and base 16.
It is a nialpdrome in base 15.
It is a zygodrome in base 14.
It is a junction number, because it is equal to n+sod(n) for n = 17793 and 17802.
It is a congruent number.
It is not an unprimeable number, because it can be changed into a prime (17827) by changing a digit.
17820 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 19 ways as a sum of consecutive naturals, for example, 1615 + ... + 1625.
217820 is an apocalyptic number.
17820 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 17820, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (30492).
17820 is an abundant number, since it is smaller than the sum of its proper divisors (43164).
It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.
17820 is a wasteful number, since it uses less digits than its factorization.
17820 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 32 (or 21 counting only the distinct ones).
The product of its (nonzero) digits is 112, while the sum is 18.
The square root of 17820 is about 133.4915727677. The cubic root of 17820 is about 26.1197630735.
17820 divided by its sum of digits (18) gives a triangular number (990 = T44).
The spelling of 17820 in words is "seventeen thousand, eight hundred twenty".
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