72128 has 42 divisors (see below), whose sum is σ = 173736. Its totient is φ = 29568.

The previous prime is 72109. The next prime is 72139. The reversal of 72128 is 82127.

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

Its product of digits (224) is a multiple of the sum of its prime divisors (32).

It is a congruent number.

It is an unprimeable number.

72128 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, 3125 + ... + 3147.

2⁷²¹²⁸ 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 72128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (86868).

72128 is an abundant number, since it is smaller than the sum of its proper divisors (101608).

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

72128 is a wasteful number, since it uses less digits than its factorization.

72128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 49 (or 32 counting only the distinct ones).

The product of its digits is 224, while the sum is 20.

The square root of 72128 is about 268.5665653055. The cubic root of 72128 is about 41.6263147117.

Subtracting 72128 from its reverse (82127), we obtain a palindrome (9999).

It can be divided in two parts, 72 and 128, that multiplied together give a square (9216 = 96²).

The spelling of 72128 in words is "seventy-two thousand, one hundred twenty-eight".