82213824 has 224 divisors, whose sum is σ = 278562816. Its totient is φ = 20782080.

The previous prime is 82213823. The next prime is 82213847. The reversal of 82213824 is 42831228.

It is a tau number, because it is divible by the number of its divisors (224).

It is a super-2 number, since 2×82213824² = 13518225713405952, which contains 22 as substring.

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

It is a junction number, because it is equal to n+sod(n) for n = 82213791 and 82213800.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82213823) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 990487 + ... + 990569.

It is an arithmetic number, because the mean of its divisors is an integer number (1243584).

Almost surely, 2^82213824 is an apocalyptic number.

82213824 is a gapful number since it is divisible by the number (84) 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 82213824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (139281408).

82213824 is an abundant number, since it is smaller than the sum of its proper divisors (196348992).

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

82213824 is a wasteful number, since it uses less digits than its factorization.

82213824 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 183 (or 173 counting only the distinct ones).

The product of its digits is 6144, while the sum is 30.

The square root of 82213824 is about 9067.1839068147. The cubic root of 82213824 is about 434.8254445633.

The spelling of 82213824 in words is "eighty-two million, two hundred thirteen thousand, eight hundred twenty-four".