82262400 has 384 divisors, whose sum is σ = 318729600. Its totient is φ = 18432000.

The previous prime is 82262377. The next prime is 82262407. The reversal of 82262400 is 426228.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (82262407) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2006380 + ... + 2006420.

It is an arithmetic number, because the mean of its divisors is an integer number (830025).

Almost surely, 2^82262400 is an apocalyptic number.

82262400 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 82262400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (159364800).

82262400 is an abundant number, since it is smaller than the sum of its proper divisors (236467200).

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

82262400 is a wasteful number, since it uses less digits than its factorization.

82262400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 98 (or 81 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 24.

The square root of 82262400 is about 9069.8621819739. The cubic root of 82262400 is about 434.9110665068.

Adding to 82262400 its reverse (426228), we get a palindrome (82688628).

The spelling of 82262400 in words is "eighty-two million, two hundred sixty-two thousand, four hundred".