37728 has 36 divisors (see below), whose sum is σ = 108108. Its totient is φ = 12480.

The previous prime is 37717. The next prime is 37747. The reversal of 37728 is 82773.

It is a tau number, because it is divible by the number of its divisors (36).

Its product of digits (2352) is a multiple of the sum of its prime factors (147).

It is a congruent number.

It is an unprimeable number.

37728 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 223 + ... + 353.

It is an arithmetic number, because the mean of its divisors is an integer number (3003).

2³⁷⁷²⁸ 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 37728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (54054).

37728 is an abundant number, since it is smaller than the sum of its proper divisors (70380).

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

37728 is a wasteful number, since it uses less digits than its factorization.

37728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 147 (or 136 counting only the distinct ones).

The product of its digits is 2352, while the sum is 27.

The square root of 37728 is about 194.2369686749. The cubic root of 37728 is about 33.5393463582.

The spelling of 37728 in words is "thirty-seven thousand, seven hundred twenty-eight".