2013 has 8 divisors (see below), whose sum is σ = 2976. Its totient is φ = 1200.

The previous prime is 2011. The next prime is 2017. The reversal of 2013 is 3102.

2013 is nontrivially palindromic in base 13.

It is a sphenic number, since it is the product of 3 distinct primes.

It is not a de Polignac number, because 2013 - 2¹ = 2011 is a prime.

It is a Curzon number.

2013 is a nontrivial repdigit in base 13.

It is a plaindrome in base 13 and base 16.

It is a nialpdrome in base 13.

It is a zygodrome in base 13.

It is a junction number, because it is equal to n+sod(n) for n = 1992 and 2010.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (2011) 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, 3 + ... + 63.

It is an arithmetic number, because the mean of its divisors is an integer number (372).

It is an amenable number.

2013 is a deficient number, since it is larger than the sum of its proper divisors (963).

2013 is a wasteful number, since it uses less digits than its factorization.

2013 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75.

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

The square root of 2013 is about 44.8664685483. The cubic root of 2013 is about 12.6264498547.

Adding to 2013 its reverse (3102), we get a palindrome (5115).

Subtracting 2013 from its reverse (3102), we obtain a square (1089 = 33²).

It can be divided in two parts, 20 and 13, that added together give a palindrome (33).

The spelling of 2013 in words is "two thousand, thirteen".