38640 has 80 divisors (see below), whose sum is σ = 142848. Its totient is φ = 8448.

The previous prime is 38639. The next prime is 38651. The reversal of 38640 is 4683.

38640 = 18² + 19² + ... + 49².

38640 is digitally balanced in base 2 and base 4, because in such bases 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 (80).

It is a Harshad number since it is a multiple of its sum of digits (21).

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 38640.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 1669 + ... + 1691.

38640 is a Friedman number, since it can be written as 30*(6^4-8), using all its digits and the basic arithmetic operations.

2³⁸⁶⁴⁰ is an apocalyptic number.

38640 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 38640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (71424).

38640 is an abundant number, since it is smaller than the sum of its proper divisors (104208).

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

38640 is a wasteful number, since it uses less digits than its factorization.

38640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 46 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 21.

The square root of 38640 is about 196.5705980049. The cubic root of 38640 is about 33.8074467446.

The spelling of 38640 in words is "thirty-eight thousand, six hundred forty".