37648 has 20 divisors (see below), whose sum is σ = 78988. Its totient is φ = 17280.

The previous prime is 37643. The next prime is 37649. The reversal of 37648 is 84673.

It can be written as a sum of positive squares in 2 ways, for example, as 2304 + 35344 = 48^2 + 188^2 .

It is a d-powerful number, because it can be written as 3⁶ + 7² + 6 + 4⁶ + 8⁵ .

It is a nialpdrome in base 16.

It is not an unprimeable number, because it can be changed into a prime (37643) by changing a digit.

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 3 ways as a sum of consecutive naturals, for example, 118 + ... + 298.

2³⁷⁶⁴⁸ 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 37648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (39494).

37648 is an abundant number, since it is smaller than the sum of its proper divisors (41340).

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

37648 is a wasteful number, since it uses less digits than its factorization.

37648 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 202 (or 196 counting only the distinct ones).

The product of its digits is 4032, while the sum is 28.

The square root of 37648 is about 194.0309253702. The cubic root of 37648 is about 33.5156235137.

It can be divided in two parts, 376 and 48, that added together give a palindrome (424).

The spelling of 37648 in words is "thirty-seven thousand, six hundred forty-eight".