82464400 has 60 divisors (see below), whose sum is σ = 204981300. Its totient is φ = 31843840.

The previous prime is 82464373. The next prime is 82464457. The reversal of 82464400 is 446428.

It can be written as a sum of positive squares in 6 ways, for example, as 8573184 + 73891216 = 2928^2 + 8596^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 8046 + ... + 15154.

It is an arithmetic number, because the mean of its divisors is an integer number (3416355).

Almost surely, 2^82464400 is an apocalyptic number.

82464400 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 82464400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (102490650).

82464400 is an abundant number, since it is smaller than the sum of its proper divisors (122516900).

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

82464400 is a wasteful number, since it uses less digits than its factorization.

82464400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 7156 (or 7145 counting only the distinct ones).

The product of its (nonzero) digits is 6144, while the sum is 28.

The square root of 82464400 is about 9080.9911353332. The cubic root of 82464400 is about 435.2667584747.

The spelling of 82464400 in words is "eighty-two million, four hundred sixty-four thousand, four hundred".