829800 has 72 divisors (see below), whose sum is σ = 2792790. Its totient is φ = 220800.

The previous prime is 829789. The next prime is 829811. The reversal of 829800 is 8928.

It is an interprime number because it is at equal distance from previous prime (829789) and next prime (829811).

It can be written as a sum of positive squares in 3 ways, for example, as 544644 + 285156 = 738^2 + 534^2 .

It is a tau number, because it is divible by the number of its divisors (72).

It is an unprimeable number.

829800 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 17 ways as a sum of consecutive naturals, for example, 1570 + ... + 2030.

2⁸²⁹⁸⁰⁰ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 829800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1396395).

829800 is an abundant number, since it is smaller than the sum of its proper divisors (1962990).

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

829800 is a wasteful number, since it uses less digits than its factorization.

829800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 483 (or 471 counting only the distinct ones).

The product of its (nonzero) digits is 1152, while the sum is 27.

The square root of 829800 is about 910.9335870413. The cubic root of 829800 is about 93.9704147123.

The spelling of 829800 in words is "eight hundred twenty-nine thousand, eight hundred".