• 963 is the smallest nontrivial such that ² ends with the reverse of . Here, 963² = 927369. The next numbers with this property are 9867 and 65766, while a much larger such number, found by Dieter Beckerle, is 42438303108538316396992097393368.

---

963 has 6 divisors (see below), whose sum is σ = 1404. Its totient is φ = 636.

The previous prime is 953. The next prime is 967. The reversal of 963 is 369.

963 is nontrivially palindromic in base 16.

963 is an esthetic number in base 5, because in such base its adjacent digits differ by 1.

It is not a de Polignac number, because 963 - 2⁴ = 947 is a prime.

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

963 is an undulating number in base 16.

It is a straight-line number, since its digits are in arithmetic progression.

It is a nialpdrome in base 10 and base 15.

It is a zygodrome in base 2.

It is not an unprimeable number, because it can be changed into a prime (967) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 45 + ... + 62.

It is an arithmetic number, because the mean of its divisors is an integer number (234).

963 is a deficient number, since it is larger than the sum of its proper divisors (441).

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

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

The sum of its prime factors is 113 (or 110 counting only the distinct ones).

The product of its digits is 162, while the sum is 18.

The square root of 963 is about 31.0322412984. The cubic root of 963 is about 9.8751134955.

It can be divided in two parts, 96 and 3, that added together give a palindrome (99).

The spelling of 963 in words is "nine hundred sixty-three", and thus it is an aban number and an oban number.