221328 has 60 divisors (see below), whose sum is σ = 652860. Its totient is φ = 69888.

The previous prime is 221327. The next prime is 221393. The reversal of 221328 is 823122.

It is a happy number.

It can be written as a sum of positive squares in 2 ways, for example, as 138384 + 82944 = 372^2 + 288^2 .

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nude number because it is divisible by every one of its digits.

It is an Ulam number.

Its product of digits (192) is a multiple of the sum of its prime factors (96).

It is a nialpdrome in base 12.

It is a self number, because there is not a number n which added to its sum of digits gives 221328.

It is not an unprimeable number, because it can be changed into a prime (221327) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 4150 + ... + 4202.

It is an arithmetic number, because the mean of its divisors is an integer number (10881).

2²²¹³²⁸ 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 221328, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (326430).

221328 is an abundant number, since it is smaller than the sum of its proper divisors (431532).

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

221328 is a wasteful number, since it uses less digits than its factorization.

221328 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 96 (or 87 counting only the distinct ones).

The product of its digits is 192, while the sum is 18.

The square root of 221328 is about 470.4550988139. The cubic root of 221328 is about 60.4893317255.

The spelling of 221328 in words is "two hundred twenty-one thousand, three hundred twenty-eight".