82764201600 has 384 divisors, whose sum is σ = 303519115200. Its totient is φ = 22024949760.

The previous prime is 82764201551. The next prime is 82764201607. The reversal of 82764201600 is 610246728.

82764201600 is a `hidden beast` number, since 8 + 2 + 7 + 6 + 42 + 0 + 1 + 600 = 666.

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 (36).

It is not an unprimeable number, because it can be changed into a prime (82764201607) 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, 73698639 + ... + 73699761.

Almost surely, 2^82764201600 is an apocalyptic number.

82764201600 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 82764201600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (151759557600).

82764201600 is an abundant number, since it is smaller than the sum of its proper divisors (220754913600).

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

82764201600 is a wasteful number, since it uses less digits than its factorization.

82764201600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2009 (or 1986 counting only the distinct ones).

The product of its (nonzero) digits is 32256, while the sum is 36.

The spelling of 82764201600 in words is "eighty-two billion, seven hundred sixty-four million, two hundred one thousand, six hundred".