827730000 has 300 divisors, whose sum is σ = 3070632708. Its totient is φ = 207360000.

The previous prime is 827729971. The next prime is 827730067. The reversal of 827730000 is 37728.

It can be written as a sum of positive squares in 10 ways, for example, as 565678656 + 262051344 = 23784^2 + 16188^2 .

It is a tau number, because it is divible by the number of its divisors (300).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 1529730 + ... + 1530270.

Almost surely, 2^827730000 is an apocalyptic number.

827730000 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 827730000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1535316354).

827730000 is an abundant number, since it is smaller than the sum of its proper divisors (2242902708).

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

827730000 is a wasteful number, since it uses less digits than its factorization.

827730000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 592 (or 568 counting only the distinct ones).

The product of its (nonzero) digits is 2352, while the sum is 27.

The square root of 827730000 is about 28770.2971830324. The cubic root of 827730000 is about 938.9221083576.

Adding to 827730000 its reverse (37728), we get a palindrome (827767728).

The spelling of 827730000 in words is "eight hundred twenty-seven million, seven hundred thirty thousand".