221408 has 48 divisors (see below), whose sum is σ = 517104. Its totient is φ = 92160.

The previous prime is 221401. The next prime is 221411. The reversal of 221408 is 804122.

It is a Harshad number since it is a multiple of its sum of digits (17).

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 221408.

It is not an unprimeable number, because it can be changed into a prime (221401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 5966 + ... + 6002.

It is an arithmetic number, because the mean of its divisors is an integer number (10773).

2²²¹⁴⁰⁸ is an apocalyptic number.

221408 is the 272-nd octagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 221408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (258552).

221408 is an abundant number, since it is smaller than the sum of its proper divisors (295696).

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

221408 is a wasteful number, since it uses less digits than its factorization.

221408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75 (or 67 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 17.

The square root of 221408 is about 470.5401151868. The cubic root of 221408 is about 60.4966188944.

It can be divided in two parts, 22 and 1408, that multiplied together give a square (30976 = 176²).

The spelling of 221408 in words is "two hundred twenty-one thousand, four hundred eight".