72000 has 84 divisors (see below), whose sum is σ = 257556. Its totient is φ = 19200.

The previous prime is 71999. The next prime is 72019. The reversal of 72000 is 27.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 2 ways, for example, as 2304 + 69696 = 48^2 + 264^2 .

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a nialpdrome in base 10.

It is a congruent number.

It is an unprimeable number.

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 11 ways as a sum of consecutive naturals, for example, 14398 + ... + 14402.

2⁷²⁰⁰⁰ 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 72000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (128778).

72000 is an abundant number, since it is smaller than the sum of its proper divisors (185556).

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

72000 is a wasteful number, since it uses less digits than its factorization.

72000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 33 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 14, while the sum is 9.

The square root of 72000 is about 268.3281573000. The cubic root of 72000 is about 41.6016764610.

Adding to 72000 its reverse (27), we get a palindrome (72027).

The spelling of 72000 in words is "seventy-two thousand", and thus it is an iban number.