31920 has 80 divisors (see below), whose sum is σ = 119040. Its totient is φ = 6912.

The previous prime is 31907. The next prime is 31957. The reversal of 31920 is 2913.

31920 = T₂₄ + T₂₅ + ... + T₅₈.

It is a tau number, because it is divible by the number of its divisors (80).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 31920.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1671 + ... + 1689.

It is an arithmetic number, because the mean of its divisors is an integer number (1488).

2³¹⁹²⁰ is an apocalyptic number.

31920 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 31920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (59520).

31920 is an abundant number, since it is smaller than the sum of its proper divisors (87120).

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

31920 is a wasteful number, since it uses less digits than its factorization.

31920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 42 (or 36 counting only the distinct ones).

The product of its (nonzero) digits is 54, while the sum is 15.

The square root of 31920 is about 178.6616914730. The cubic root of 31920 is about 31.7215422773.

The spelling of 31920 in words is "thirty-one thousand, nine hundred twenty".