82314000 has 240 divisors, whose sum is σ = 305538480. Its totient is φ = 20582400.

The previous prime is 82313999. The next prime is 82314031. The reversal of 82314000 is 41328.

It is a happy number.

It can be written as a sum of positive squares in 8 ways, for example, as 35856144 + 46457856 = 5988^2 + 6816^2 .

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (18).

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, 305866 + ... + 306134.

It is an arithmetic number, because the mean of its divisors is an integer number (1273077).

Almost surely, 2^82314000 is an apocalyptic number.

82314000 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 82314000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (152769240).

82314000 is an abundant number, since it is smaller than the sum of its proper divisors (223224480).

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

82314000 is a wasteful number, since it uses less digits than its factorization.

82314000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 315 (or 296 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 82314000 is about 9072.7063217102. The cubic root of 82314000 is about 435.0019817587.

Adding to 82314000 its reverse (41328), we get a palindrome (82355328).

The spelling of 82314000 in words is "eighty-two million, three hundred fourteen thousand".