37828 has 18 divisors (see below), whose sum is σ = 77406. Its totient is φ = 16128.

The previous prime is 37813. The next prime is 37831. The reversal of 37828 is 82873.

It is a happy number.

It can be written as a sum of positive squares in only one way, i.e., 28224 + 9604 = 168^2 + 98^2 .

It is a Harshad number since it is a multiple of its sum of digits (28).

It is an Ulam number.

It is a nialpdrome in base 14.

It is a junction number, because it is equal to n+sod(n) for n = 37796 and 37805.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 100 + ... + 292.

2³⁷⁸²⁸ 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 37828, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (38703).

37828 is an abundant number, since it is smaller than the sum of its proper divisors (39578).

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

37828 is a wasteful number, since it uses less digits than its factorization.

With its successor (37829) it forms a Ruth-Aaron pair, since the sum of their prime factors is the same (211).

37828 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 211 (or 202 counting only the distinct ones).

The product of its digits is 2688, while the sum is 28.

The square root of 37828 is about 194.4942158523. The cubic root of 37828 is about 33.5689528020.

It can be divided in two parts, 378 and 28, that added together give a triangular number (406 = T₂₈).

The spelling of 37828 in words is "thirty-seven thousand, eight hundred twenty-eight".