81705600 has 144 divisors (see below), whose sum is σ = 291647070. Its totient is φ = 21780480.

The previous prime is 81705571. The next prime is 81705623. The reversal of 81705600 is 650718.

It can be written as a sum of positive squares in 3 ways, for example, as 36869184 + 44836416 = 6072^2 + 6696^2 .

It is a tau number, because it is divible by the number of its divisors (144).

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 17 ways as a sum of consecutive naturals, for example, 27382 + ... + 30218.

Almost surely, 2^81705600 is an apocalyptic number.

81705600 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 81705600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (145823535).

81705600 is an abundant number, since it is smaller than the sum of its proper divisors (209941470).

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

81705600 is a wasteful number, since it uses less digits than its factorization.

81705600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2867 (or 2847 counting only the distinct ones).

The product of its (nonzero) digits is 1680, while the sum is 27.

The square root of 81705600 is about 9039.1150009279. The cubic root of 81705600 is about 433.9276001749.

It can be divided in two parts, 81 and 705600, that multiplied together give a square (57153600 = 7560²).

The spelling of 81705600 in words is "eighty-one million, seven hundred five thousand, six hundred".