• 33 can be written using four 4's:

• Deleting all the even digits from 2^{33} = 8589934592 we obtain a prime (599359).

33 has 4 divisors (see below), whose sum is σ = 48. Its totient is φ = 20.

The previous prime is 31. The next prime is 37.

Added to its reverse (33) it gives a triangular number (66 = T_{11}).

33 is nontrivially palindromic in base 2 and base 10.

It is a Cunningham number, because it is equal to 2^{5}+1.

33 is an esthetic number in base 7, base 15 and base 16, because in such bases its adjacent digits differ by 1.

It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4.

It is a cyclic number.

It is not a de Polignac number, because 33 - 2^{1} = 31 is a prime.

It is a nude number because it is divisible by every one of its digits.

33 is an idoneal number.

It is a D-number.

It is a Curzon number.

33 is a lucky number.

33 is a nontrivial repdigit in base 10.

It is a plaindrome in base 5, base 7, base 9, base 10, base 12, base 13, base 14 and base 15.

It is a nialpdrome in base 6, base 8, base 10, base 11 and base 16.

It is a zygodrome in base 10.

It is a pernicious number, because its binary representation contains a prime number (2) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 3 + ... + 8.

It is an arithmetic number, because the mean of its divisors is an integer number (12).

It is a Proth number, since it is equal to 1 ⋅ 2^{5} + 1 and 1 < 2^{5}.

It is an amenable number.

33 is a deficient number, since it is larger than the sum of its proper divisors (15).

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

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

The sum of its prime factors is 14.

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

The square root of 33 is about 5.7445626465. The cubic root of 33 is about 3.2075343300.

The spelling of 33 in words is "thirty-three", and thus it is an aban number, an oban number, and an uban number.

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