82359984 has 180 divisors, whose sum is σ = 263904984. Its totient is φ = 22063104.

The previous prime is 82359983. The next prime is 82359989. The reversal of 82359984 is 48995328.

It is a Harshad number since it is a multiple of its sum of digits (48).

Its product of digits (622080) is a multiple of the sum of its prime divisors (128).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82359983) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 849024 + ... + 849120.

Almost surely, 2^82359984 is an apocalyptic number.

82359984 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 82359984, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (131952492).

82359984 is an abundant number, since it is smaller than the sum of its proper divisors (181545000).

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

82359984 is a wasteful number, since it uses less digits than its factorization.

82359984 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 160 (or 128 counting only the distinct ones).

The product of its digits is 622080, while the sum is 48.

The square root of 82359984 is about 9075.2401621114. The cubic root of 82359984 is about 435.0829700370.

The spelling of 82359984 in words is "eighty-two million, three hundred fifty-nine thousand, nine hundred eighty-four".