37820 has 24 divisors (see below), whose sum is σ = 83328. Its totient is φ = 14400.

The previous prime is 37813. The next prime is 37831. The reversal of 37820 is 2873.

37820 = T₁ + T₂ + ... + T₆₀.

37820 = 9² + 10² + ... + 48².

37820 is nontrivially palindromic in base 11.

37820 is digitally balanced in base 6, because in such base it contains all the possibile digits an equal number of times.

37820 is a nontrivial binomial coefficient, being equal to C(62, 3).

It is a Smith number, since the sum of its digits (20) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (20).

37820 is strictly pandigital in base 6.

It is a junction number, because it is equal to n+sod(n) for n = 37792 and 37801.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 37820.

It is an unprimeable number.

It is the 60-th tetrahedral number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 590 + ... + 650.

It is an arithmetic number, because the mean of its divisors is an integer number (3472).

2³⁷⁸²⁰ 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 37820, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (41664).

37820 is an abundant number, since it is smaller than the sum of its proper divisors (45508).

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

37820 is a wasteful number, since it uses less digits than its factorization.

37820 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 101 (or 99 counting only the distinct ones).

The product of its (nonzero) digits is 336, while the sum is 20.

The square root of 37820 is about 194.4736486005. The cubic root of 37820 is about 33.5665862079.

37820 divided by its sum of digits (20) gives a triangular number (1891 = T₆₁).

The spelling of 37820 in words is "thirty-seven thousand, eight hundred twenty".