64000 has 40 divisors (see below), whose sum is σ = 159588. Its totient is φ = 25600.

The previous prime is 63997. The next prime is 64007. The reversal of 64000 is 46.

64000 = 3³ + 4³ + ... + 22³.

The cubic root of 64000 is 40.

It is a perfect power (a cube), and thus also a powerful number.

It can be written as a sum of positive squares in 2 ways, for example, as 43264 + 20736 = 208^2 + 144^2 .

It is a tau number, because it is divible by the number of its divisors (40).

It is a Harshad number since it is a multiple of its sum of digits (10).

It is a nialpdrome in base 4, base 10 and base 16.

It is a zygodrome in base 4.

It is not an unprimeable number, because it can be changed into a prime (64007) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 12798 + ... + 12802.

2⁶⁴⁰⁰⁰ 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 64000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (79794).

64000 is an abundant number, since it is smaller than the sum of its proper divisors (95588).

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

64000 is an frugal number, since it uses more digits than its factorization.

64000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 33 (or 7 counting only the distinct ones).

The product of its (nonzero) digits is 24, while the sum is 10.

The square root of 64000 is about 252.9822128135.

Multiplying 64000 by its sum of digits (10), we get a square (640000 = 800²).

64000 divided by its sum of digits (10) gives a square (6400 = 80²).

Adding to 64000 its reverse (46), we get a palindrome (64046).

The spelling of 64000 in words is "sixty-four thousand", and thus it is an eban number.