32767 has 8 divisors (see below), whose sum is σ = 38912. Its totient is φ = 27000.

The previous prime is 32749. The next prime is 32771. The reversal of 32767 is 76723.

32767 is nontrivially palindromic in base 2 and base 8.

It is a Cunningham number, because it is equal to 2¹⁵-1.

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

It is a cyclic number.

It is a de Polignac number, because none of the positive numbers 2^k-32767 is a prime.

It is a super-5 number, since 5×32767⁵ (a number of 24 digits) contains 55555 as substring.

It is an alternating number because its digits alternate between odd and even.

It is a Duffinian number.

32767 is a nontrivial repdigit in base 2 and base 8.

It is a plaindrome in base 2, base 4, base 8, base 11 and base 16.

It is a nialpdrome in base 2 and base 8.

It is a zygodrome in base 2 and base 8.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 32767.

It is not an unprimeable number, because it can be changed into a prime (32707) by changing a digit.

It is a nontrivial repunit in base 2.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 142 + ... + 292.

It is an arithmetic number, because the mean of its divisors is an integer number (4864).

2³²⁷⁶⁷ is an apocalyptic number.

32767 is a deficient number, since it is larger than the sum of its proper divisors (6145).

32767 is a wasteful number, since it uses less digits than its factorization.

32767 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 189.

The product of its digits is 1764, while the sum is 25.

The square root of 32767 is about 181.0165738268. The cubic root of 32767 is about 31.9996744759. Note that the first 3 decimals are identical.

Subtracting 32767 from its reverse (76723), we obtain a triangular number (43956 = T₂₉₆).

The spelling of 32767 in words is "thirty-two thousand, seven hundred sixty-seven".