33000 has 64 divisors (see below), whose sum is σ = 112320. Its totient is φ = 8000.

The previous prime is 32999. The next prime is 33013. The reversal of 33000 is 33.

It is a Harshad number since it is a multiple of its sum of digits (6).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

It is a nialpdrome in base 10.

It is a zygodrome in base 10.

It is a self number, because there is not a number *n* which added to its sum of digits gives 33000.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 2995 + ... + 3005.

It is an arithmetic number, because the mean of its divisors is an integer number (1755).

2^{33000} is an apocalyptic number.

33000 is a gapful number since it is divisible by the number (30) 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 33000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (56160).

33000 is an abundant number, since it is smaller than the sum of its proper divisors (79320).

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

33000 is a wasteful number, since it uses less digits than its factorization.

33000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 35 (or 21 counting only the distinct ones).

The product of its (nonzero) digits is 9, while the sum is 6.

The square root of 33000 is about 181.6590212458. The cubic root of 33000 is about 32.0753433000.

Adding to 33000 its reverse (33), we get a palindrome (33033).

33000 divided by its reverse (33) gives a cube (1000 = 10^{3}).

It can be divided in two parts, 3 and 3000, that added together give a palindrome (3003).

The spelling of 33000 in words is "thirty-three thousand".

Divisors: 1 2 3 4 5 6 8 10 11 12 15 20 22 24 25 30 33 40 44 50 55 60 66 75 88 100 110 120 125 132 150 165 200 220 250 264 275 300 330 375 440 500 550 600 660 750 825 1000 1100 1320 1375 1500 1650 2200 2750 3000 3300 4125 5500 6600 8250 11000 16500 33000

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