77224 has 24 divisors (see below), whose sum is σ = 169290. Its totient is φ = 32928.

The previous prime is 77213. The next prime is 77237. The reversal of 77224 is 42277.

77224 is nontrivially palindromic in base 5.

It can be written as a sum of positive squares in only one way, i.e., 44100 + 33124 = 210^2 + 182^2 .

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

It is a nialpdrome in base 7.

It is a zygodrome in base 7.

It is a junction number, because it is equal to n+sod(n) for n = 77195 and 77204.

It is an unprimeable number.

77224 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, 294 + ... + 490.

2⁷⁷²²⁴ 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 77224, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (84645).

77224 is an abundant number, since it is smaller than the sum of its proper divisors (92066).

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

77224 is a wasteful number, since it uses less digits than its factorization.

77224 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 217 (or 206 counting only the distinct ones).

The product of its digits is 784, while the sum is 22.

The square root of 77224 is about 277.8920653779. The cubic root of 77224 is about 42.5844227323.

It can be divided in two parts, 772 and 24, that multiplied together give a triangular number (18528 = T₁₉₂).

The spelling of 77224 in words is "seventy-seven thousand, two hundred twenty-four", and thus it is an iban number.