829757028100 has 675 divisors, whose sum is σ = 2501259951001. Its totient is φ = 238731292800.

The previous prime is 829757028071. The next prime is 829757028119. The reversal of 829757028100 is 1820757928.

The square root of 829757028100 is 910910.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 7 ways, for example, as 814120025796 + 15637002304 = 902286^2 + 125048^2 .

It is a super-2 number, since 2×829757028100² (a number of 25 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (49).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 224 ways as a sum of consecutive naturals, for example, 63827463694 + ... + 63827463706.

Almost surely, 2^829757028100 is an apocalyptic number.

829757028100 is the 910910-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 829757028100

829757028100 is an abundant number, since it is smaller than the sum of its proper divisors (1671502922901).

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

829757028100 is an equidigital number, since it uses as much as digits as its factorization.

829757028100 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 116 (or 38 counting only the distinct ones).

The product of its (nonzero) digits is 564480, while the sum is 49.

Multiplying 829757028100 by its sum of digits (49), we get a square (40658094376900 = 6376370²).

829757028100 divided by its sum of digits (49) gives a square (16933816900 = 130130²).

The spelling of 829757028100 in words is "eight hundred twenty-nine billion, seven hundred fifty-seven million, twenty-eight thousand, one hundred".