82879200 has 180 divisors, whose sum is σ = 302480640. Its totient is φ = 22083840.

The previous prime is 82879193. The next prime is 82879207. The reversal of 82879200 is 297828.

It is an interprime number because it is at equal distance from previous prime (82879193) and next prime (82879207).

It is a tau number, because it is divible by the number of its divisors (180).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82879207) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 64161 + ... + 65439.

It is an arithmetic number, because the mean of its divisors is an integer number (1680448).

Almost surely, 2^82879200 is an apocalyptic number.

82879200 is a gapful number since it is divisible by the number (80) 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 82879200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (151240320).

82879200 is an abundant number, since it is smaller than the sum of its proper divisors (219601440).

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

82879200 is a wasteful number, since it uses less digits than its factorization.

82879200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1311 (or 1289 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

The square root of 82879200 is about 9103.8014038093. The cubic root of 82879200 is about 435.9953426543.

The spelling of 82879200 in words is "eighty-two million, eight hundred seventy-nine thousand, two hundred".