72963 has 18 divisors (see below), whose sum is σ = 117572. Its totient is φ = 43560.

The previous prime is 72959. The next prime is 72973. The reversal of 72963 is 36927.

It is not a de Polignac number, because 72963 - 2² = 72959 is a prime.

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

It is a Duffinian number.

Its product of digits (2268) is a multiple of the sum of its prime divisors (81).

It is not an unprimeable number, because it can be changed into a prime (72923) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 1056 + ... + 1122.

2⁷²⁹⁶³ is an apocalyptic number.

72963 is a deficient number, since it is larger than the sum of its proper divisors (44609).

72963 is a wasteful number, since it uses less digits than its factorization.

72963 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 95 (or 81 counting only the distinct ones).

The product of its digits is 2268, while the sum is 27.

The square root of 72963 is about 270.1166414718. The cubic root of 72963 is about 41.7863297865.

It can be divided in two parts, 72 and 963, that added together give a triangular number (1035 = T₄₅).

The spelling of 72963 in words is "seventy-two thousand, nine hundred sixty-three".