4416 has 28 divisors (see below), whose sum is σ = 12192. Its totient is φ = 1408.

The previous prime is 4409. The next prime is 4421. The reversal of 4416 is 6144.

4416 = 18² + 19² + ... + 26².

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.

It is a plaindrome in base 11.

It is a zygodrome in base 11.

It is a junction number, because it is equal to n+sod(n) for n = 4395 and 4404.

It is a congruent number.

It is an unprimeable number.

4416 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 181 + ... + 203.

2⁴⁴¹⁶ is an apocalyptic number.

4416 is a gapful number since it is divisible by the number (46) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 4416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6096).

4416 is an abundant number, since it is smaller than the sum of its proper divisors (7776).

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

4416 is a wasteful number, since it uses less digits than its factorization.

4416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 38 (or 28 counting only the distinct ones).

The product of its digits is 96, while the sum is 15.

The square root of 4416 is about 66.4529909033. The cubic root of 4416 is about 16.4062637188.

Subtracting 4416 from its reverse (6144), we obtain a cube (1728 = 12³).

The spelling of 4416 in words is "four thousand, four hundred sixteen".