31968 has 48 divisors (see below), whose sum is σ = 95760. Its totient is φ = 10368.

The previous prime is 31963. The next prime is 31973. The reversal of 31968 is 86913.

31968 is nontrivially palindromic in base 11.

It is an interprime number because it is at equal distance from previous prime (31963) and next prime (31973).

It is a tau number, because it is divible by the number of its divisors (48).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nude number because it is divisible by every one of its digits.

It is one of the 548 Lynch-Bell numbers.

It is a zygodrome in base 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (31963) 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, 846 + ... + 882.

It is an arithmetic number, because the mean of its divisors is an integer number (1995).

2^{31968} is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 31968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (47880).

31968 is an abundant number, since it is smaller than the sum of its proper divisors (63792).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

31968 is a wasteful number, since it uses less digits than its factorization.

31968 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 56 (or 42 counting only the distinct ones).

The product of its digits is 1296, while the sum is 27.

The square root of 31968 is about 178.7959731090. The cubic root of 31968 is about 31.7374348362.

Subtracting 31968 from its reverse (86913), we obtain a palindrome (54945).

It can be divided in two parts, 31 and 968, that added together give a palindrome (999).

The spelling of 31968 in words is "thirty-one thousand, nine hundred sixty-eight".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 37 48 54 72 74 96 108 111 144 148 216 222 288 296 333 432 444 592 666 864 888 999 1184 1332 1776 1998 2664 3552 3996 5328 7992 10656 15984 31968

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