4224 has 32 divisors (see below), whose sum is σ = 12240. Its totient is φ = 1280.

The previous prime is 4219. The next prime is 4229.

4224 is nontrivially palindromic in base 10.

It is a Cunningham number, because it is equal to 65^{2}-1.

It is an interprime number because it is at equal distance from previous prime (4219) and next prime (4229).

It is a tau number, because it is divible by the number of its divisors (32).

It is a Harshad number since it is a multiple of its sum of digits (12).

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 d-powerful number, because it can be written as **4**^{3} + **2**^{11} + **2**^{11} + **4**^{3} .

Its product of digits (64) is a multiple of the sum of its prime divisors (16).

It is a plaindrome in base 5, base 13 and base 14.

It is a zygodrome in base 5.

It is not an unprimeable number, because it can be changed into a prime (4229) by changing a digit.

4224 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 (2) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 379 + ... + 389.

4224 is a gapful number since it is divisible by the number (44) formed by its first and last digit.

4224 is a droll number since its even prime factors and its odd prime factors have the same sum.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 4224, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (6120).

4224 is an abundant number, since it is smaller than the sum of its proper divisors (8016).

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

4224 is a wasteful number, since it uses less digits than its factorization.

4224 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 28 (or 16 counting only the distinct ones).

The product of its digits is 64, while the sum is 12.

The square root of 4224 is about 64.9923072371. The cubic root of 4224 is about 16.1649600825.

4224 divided by its product of digits (64) gives a palindrome (66).

It can be divided in two parts, 42 and 24, that added together give a palindrome (66).

The spelling of 4224 in words is "four thousand, two hundred twenty-four", and thus it is an iban number.

Divisors: 1 2 3 4 6 8 11 12 16 22 24 32 33 44 48 64 66 88 96 128 132 176 192 264 352 384 528 704 1056 1408 2112 4224

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