829764000 has 480 divisors, whose sum is σ = 3296429136. Its totient is φ = 203212800.

The previous prime is 829763993. The next prime is 829764017. The reversal of 829764000 is 467928.

829764000 is a `hidden beast` number, since 8 + 2 + 9 + 7 + 640 + 0 + 0 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 75272976 + 754491024 = 8676^2 + 27468^2 .

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (36).

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 79 ways as a sum of consecutive naturals, for example, 4211902 + ... + 4212098.

Almost surely, 2^829764000 is an apocalyptic number.

829764000 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 829764000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1648214568).

829764000 is an abundant number, since it is smaller than the sum of its proper divisors (2466665136).

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

829764000 is a wasteful number, since it uses less digits than its factorization.

829764000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 247 (or 220 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The square root of 829764000 is about 28805.6244507909. The cubic root of 829764000 is about 939.6905575681.

The spelling of 829764000 in words is "eight hundred twenty-nine million, seven hundred sixty-four thousand".