829440000 has 375 divisors, whose sum is σ = 3096514267. Its totient is φ = 221184000.

The previous prime is 829439987. The next prime is 829440037. The reversal of 829440000 is 44928.

The square root of 829440000 is 28800.

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

It is a Jordan-Polya number, since it can be written as (5!)⁴ ⋅ (2!)².

It can be written as a sum of positive squares in 2 ways, for example, as 65028096 + 764411904 = 8064^2 + 27648^2 .

It is a tau number, because it is divible by the number of its divisors (375).

It is an ABA number since it can be written as A⋅B^A, here for A=4, B=120.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a Duffinian number.

It is a Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 1200 × 720 × 960.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 24 ways as a sum of consecutive naturals, for example, 165887998 + ... + 165888002.

Almost surely, 2^829440000 is an apocalyptic number.

829440000 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

829440000 is the 28800-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 829440000

829440000 is an abundant number, since it is smaller than the sum of its proper divisors (2267074267).

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

829440000 is an frugal number, since it uses more digits than its factorization.

829440000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 60 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The cubic root of 829440000 is about 939.5682338805.

Multiplying 829440000 by its product of nonzero digits (2304), we get a square (1911029760000 = 1382400²).

829440000 divided by its product of nonzero digits (2304) gives a square (360000 = 600²).

Adding to 829440000 its reverse (44928), we get a palindrome (829484928).

The spelling of 829440000 in words is "eight hundred twenty-nine million, four hundred forty thousand".