82772098560 has 960 divisors, whose sum is σ = 321729408000. Its totient is φ = 20328579072.

The previous prime is 82772098501. The next prime is 82772098621. The reversal of 82772098560 is 6589027728.

It is a happy number.

82772098560 is a `hidden beast` number, since 8 + 2 + 7 + 72 + 0 + 9 + 8 + 560 = 666.

It is a tau number, because it is divible by the number of its divisors (960).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a junction number, because it is equal to n+sod(n) for n = 82772098497 and 82772098506.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 555517366 + ... + 555517514.

It is an arithmetic number, because the mean of its divisors is an integer number (335134800).

Almost surely, 2^82772098560 is an apocalyptic number.

82772098560 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 82772098560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (160864704000).

82772098560 is an abundant number, since it is smaller than the sum of its proper divisors (238957309440).

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

82772098560 is a wasteful number, since it uses less digits than its factorization.

82772098560 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 253 (or 225 counting only the distinct ones).

The product of its (nonzero) digits is 3386880, while the sum is 54.

The spelling of 82772098560 in words is "eighty-two billion, seven hundred seventy-two million, ninety-eight thousand, five hundred sixty".