828960 has 96 divisors (see below), whose sum is σ = 2866752. Its totient is φ = 199680.

The previous prime is 828953. The next prime is 828967. The reversal of 828960 is 69828.

It is an interprime number because it is at equal distance from previous prime (828953) and next prime (828967).

It is a tau number, because it is divible by the number of its divisors (96).

It is a Smith number, since the sum of its digits (33) coincides with the sum of the digits of its prime factors.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is a nialpdrome in base 16.

It is not an unprimeable number, because it can be changed into a prime (828967) by changing a digit.

828960 is an untouchable number, because it is not equal to the sum of proper divisors of any 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 15 ways as a sum of consecutive naturals, for example, 5202 + ... + 5358.

It is an arithmetic number, because the mean of its divisors is an integer number (29862).

2⁸²⁸⁹⁶⁰ is an apocalyptic number.

828960 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 828960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1433376).

828960 is an abundant number, since it is smaller than the sum of its proper divisors (2037792).

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

828960 is a wasteful number, since it uses less digits than its factorization.

828960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 186 (or 178 counting only the distinct ones).

The product of its (nonzero) digits is 6912, while the sum is 33.

The square root of 828960 is about 910.4724048537. The cubic root of 828960 is about 93.9386955035.

The spelling of 828960 in words is "eight hundred twenty-eight thousand, nine hundred sixty".