829920 has 192 divisors, whose sum is σ = 3386880. Its totient is φ = 165888.

The previous prime is 829883. The next prime is 829949. The reversal of 829920 is 29928.

It is a Cunningham number, because it is equal to 911²-1.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

829920 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 43671 + ... + 43689.

It is an arithmetic number, because the mean of its divisors is an integer number (17640).

2⁸²⁹⁹²⁰ is an apocalyptic number.

829920 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 829920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1693440).

829920 is an abundant number, since it is smaller than the sum of its proper divisors (2556960).

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

829920 is a wasteful number, since it uses less digits than its factorization.

829920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 57 (or 49 counting only the distinct ones).

The product of its (nonzero) digits is 2592, while the sum is 30.

The square root of 829920 is about 910.9994511524. Note that the first 3 decimals coincide. The cubic root of 829920 is about 93.9749442802.

The spelling of 829920 in words is "eight hundred twenty-nine thousand, nine hundred twenty".