82764000 has 432 divisors, whose sum is σ = 339852240. Its totient is φ = 19008000.

The previous prime is 82763957. The next prime is 82764043. The reversal of 82764000 is 46728.

It is an interprime number because it is at equal distance from previous prime (82763957) and next prime (82764043).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 4355991 + ... + 4356009.

It is an arithmetic number, because the mean of its divisors is an integer number (786695).

Almost surely, 2^82764000 is an apocalyptic number.

82764000 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 82764000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (169926120).

82764000 is an abundant number, since it is smaller than the sum of its proper divisors (257088240).

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

82764000 is a wasteful number, since it uses less digits than its factorization.

82764000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 72 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 2688, while the sum is 27.

The square root of 82764000 is about 9097.4721763795. The cubic root of 82764000 is about 435.7932414728.

The spelling of 82764000 in words is "eighty-two million, seven hundred sixty-four thousand".