82844985600 has 1080 divisors, whose sum is σ = 347777115840. Its totient is φ = 19289456640.

The previous prime is 82844985571. The next prime is 82844985611. The reversal of 82844985600 is 658944828.

82844985600 is a `hidden beast` number, since 8 + 28 + 4 + 4 + 9 + 8 + 5 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (1080).

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

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 128044477 + ... + 128045123.

It is an arithmetic number, because the mean of its divisors is an integer number (322015848).

Almost surely, 2^82844985600 is an apocalyptic number.

82844985600 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 82844985600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (173888557920).

82844985600 is an abundant number, since it is smaller than the sum of its proper divisors (264932130240).

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

82844985600 is a wasteful number, since it uses less digits than its factorization.

82844985600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 717 (or 689 counting only the distinct ones).

The product of its (nonzero) digits is 4423680, while the sum is 54.

The spelling of 82844985600 in words is "eighty-two billion, eight hundred forty-four million, nine hundred eighty-five thousand, six hundred".