82760740966800 has 1200 divisors, whose sum is σ = 340561852302672. Its totient is φ = 19067299430400.

The previous prime is 82760740966793. The next prime is 82760740966823. The reversal of 82760740966800 is 866904706728.

82760740966800 is a `hidden beast` number, since 82 + 76 + 0 + 7 + 409 + 6 + 6 + 80 + 0 = 666.

It can be written as a sum of positive squares in 24 ways, for example, as 73398903443856 + 9361837522944 = 8567316^2 + 3059712^2 .

It is a tau number, because it is divible by the number of its divisors (1200).

It is an unprimeable number.

It is a polite number, since it can be written in 239 ways as a sum of consecutive naturals, for example, 1296000472 + ... + 1296064328.

Almost surely, 2^{82760740966800} is an apocalyptic number.

82760740966800 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 82760740966800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (170280926151336).

82760740966800 is an abundant number, since it is smaller than the sum of its proper divisors (257801111335872).

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

82760740966800 is a wasteful number, since it uses less digits than its factorization.

82760740966800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 64098 (or 64078 counting only the distinct ones).

The product of its (nonzero) digits is 48771072, while the sum is 63.

The spelling of 82760740966800 in words is "eighty-two trillion, seven hundred sixty billion, seven hundred forty million, nine hundred sixty-six thousand, eight hundred".