331920 has 60 divisors (see below), whose sum is σ = 1117116. Its totient is φ = 88320.

The previous prime is 331909. The next prime is 331921. The reversal of 331920 is 29133.

It can be written as a sum of positive squares in 2 ways, for example, as 112896 + 219024 = 336^2 + 468^2 .

It is a tau number, because it is divible by the number of its divisors (60).

It is a super-2 number, since 2×331920² = 220341772800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a junction number, because it is equal to n+sod(n) for n = 331893 and 331902.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 331920.

It is not an unprimeable number, because it can be changed into a prime (331921) by changing a digit.

331920 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 490 + ... + 950.

2³³¹⁹²⁰ is an apocalyptic number.

331920 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 331920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (558558).

331920 is an abundant number, since it is smaller than the sum of its proper divisors (785196).

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

331920 is a wasteful number, since it uses less digits than its factorization.

331920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 480 (or 471 counting only the distinct ones).

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

The square root of 331920 is about 576.1249864396. The cubic root of 331920 is about 69.2379935481.

It can be divided in two parts, 33 and 1920, that added together give a triangular number (1953 = T₆₂).

The spelling of 331920 in words is "three hundred thirty-one thousand, nine hundred twenty".