82814400 has 294 divisors, whose sum is σ = 309826152. Its totient is φ = 21772800.

The previous prime is 82814387. The next prime is 82814419. The reversal of 82814400 is 441828.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 41 ways as a sum of consecutive naturals, for example, 1166365 + ... + 1166435.

Almost surely, 2^82814400 is an apocalyptic number.

82814400 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 82814400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (154913076).

82814400 is an abundant number, since it is smaller than the sum of its proper divisors (227011752).

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

82814400 is an equidigital number, since it uses as much as digits as its factorization.

82814400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 111 (or 81 counting only the distinct ones).

The product of its (nonzero) digits is 2048, while the sum is 27.

The square root of 82814400 is about 9100.2417550305. The cubic root of 82814400 is about 435.8816838007.

The spelling of 82814400 in words is "eighty-two million, eight hundred fourteen thousand, four hundred".