82790400 has 432 divisors, whose sum is σ = 347321520. Its totient is φ = 17203200.

The previous prime is 82790387. The next prime is 82790401. The reversal of 82790400 is 409728.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is not an unprimeable number, because it can be changed into a prime (82790401) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 7526395 + ... + 7526405.

It is an arithmetic number, because the mean of its divisors is an integer number (803985).

Almost surely, 2^82790400 is an apocalyptic number.

82790400 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 82790400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (173660760).

82790400 is an abundant number, since it is smaller than the sum of its proper divisors (264531120).

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

82790400 is a wasteful number, since it uses less digits than its factorization.

82790400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 60 (or 28 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 30.

The square root of 82790400 is about 9098.9230131923. The cubic root of 82790400 is about 435.8395728830.

The spelling of 82790400 in words is "eighty-two million, seven hundred ninety thousand, four hundred".