829832640 has 672 divisors, whose sum is σ = 3502517760. Its totient is φ = 164634624.

The previous prime is 829832639. The next prime is 829832671. The reversal of 829832640 is 46238928.

829832640 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a tau number, because it is divible by the number of its divisors (672).

It is a Harshad number since it is a multiple of its sum of digits (42).

It is a junction number, because it is equal to n+sod(n) for n = 829832592 and 829832601.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 14064931 + ... + 14064989.

It is an arithmetic number, because the mean of its divisors is an integer number (5212080).

Almost surely, 2^829832640 is an apocalyptic number.

829832640 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 829832640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1751258880).

829832640 is an abundant number, since it is smaller than the sum of its proper divisors (2672685120).

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

829832640 is a wasteful number, since it uses less digits than its factorization.

829832640 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 129 (or 112 counting only the distinct ones).

The product of its (nonzero) digits is 165888, while the sum is 42.

The square root of 829832640 is about 28806.8158601398. The cubic root of 829832640 is about 939.7164679802.

The spelling of 829832640 in words is "eight hundred twenty-nine million, eight hundred thirty-two thousand, six hundred forty".