37920 has 48 divisors (see below), whose sum is σ = 120960. Its totient is φ = 9984.

The previous prime is 37907. The next prime is 37951. The reversal of 37920 is 2973.

37920 is digitally balanced in base 6, because in such base it contains all the possibile digits an equal number of times.

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

37920 is strictly pandigital in base 6.

It is a nialpdrome in base 16.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 37920.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 441 + ... + 519.

It is an arithmetic number, because the mean of its divisors is an integer number (2520).

2³⁷⁹²⁰ is an apocalyptic number.

37920 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 37920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (60480).

37920 is an abundant number, since it is smaller than the sum of its proper divisors (83040).

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

37920 is a wasteful number, since it uses less digits than its factorization.

37920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 97 (or 89 counting only the distinct ones).

The product of its (nonzero) digits is 378, while the sum is 21.

The square root of 37920 is about 194.7305831142. The cubic root of 37920 is about 33.5961446824.

The spelling of 37920 in words is "thirty-seven thousand, nine hundred twenty".