1305 has 12 divisors (see below), whose sum is σ = 2340. Its totient is φ = 672.

The previous prime is 1303. The next prime is 1307. The reversal of 1305 is 5031.

1305 is nontrivially palindromic in base 12.

It is an interprime number because it is at equal distance from previous prime (1303) and next prime (1307).

It can be written as a sum of positive squares in 2 ways, for example, as 576 + 729 = 24^2 + 27^2 .

It is not a de Polignac number, because 1305 - 2¹ = 1303 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (9).

1305 is an undulating number in base 12.

It is a nialpdrome in base 11.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1301) by changing a digit.

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 11 ways as a sum of consecutive naturals, for example, 31 + ... + 59.

It is an arithmetic number, because the mean of its divisors is an integer number (195).

2¹³⁰⁵ is an apocalyptic number.

1305 is a gapful number since it is divisible by the number (15) formed by its first and last digit.

It is an amenable number.

1305 is a deficient number, since it is larger than the sum of its proper divisors (1035).

1305 is a wasteful number, since it uses less digits than its factorization.

1305 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 40 (or 37 counting only the distinct ones).

The product of its (nonzero) digits is 15, while the sum is 9.

The square root of 1305 is about 36.1247837364. The cubic root of 1305 is about 10.9279031466.

Adding to 1305 its reverse (5031), we get a palindrome (6336).

The spelling of 1305 in words is "one thousand, three hundred five".