82468800 has 336 divisors, whose sum is σ = 317479680. Its totient is φ = 20782080.

The previous prime is 82468787. The next prime is 82468829. The reversal of 82468800 is 886428.

It is a super-2 number, since 2×82468800² = 13602205946880000, which contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 993559 + ... + 993641.

It is an arithmetic number, because the mean of its divisors is an integer number (944880).

Almost surely, 2^82468800 is an apocalyptic number.

82468800 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 82468800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (158739840).

82468800 is an abundant number, since it is smaller than the sum of its proper divisors (235010880).

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

82468800 is a wasteful number, since it uses less digits than its factorization.

82468800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 137 (or 116 counting only the distinct ones).

The product of its (nonzero) digits is 24576, while the sum is 36.

The square root of 82468800 is about 9081.2333964060. The cubic root of 82468800 is about 435.2744997532.

The spelling of 82468800 in words is "eighty-two million, four hundred sixty-eight thousand, eight hundred".