829440 has 120 divisors (see below), whose sum is σ = 2972970. Its totient is φ = 221184.

The previous prime is 829399. The next prime is 829453. The reversal of 829440 is 44928.

It is a Jordan-Polya number, since it can be written as 6! ⋅ (4!)² ⋅ 2!.

It can be written as a sum of positive squares in only one way, i.e., 746496 + 82944 = 864^2 + 288^2 .

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nialpdrome in base 16.

It is a Saint-Exupery number, since it is equal to the product of the sides of a Pythagorean triangle: 120 × 72 × 96.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 829440.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 165886 + ... + 165890.

829440 is a Friedman number, since it can be written as 40*(9*8)^2*4, using all its digits and the basic arithmetic operations.

2⁸²⁹⁴⁴⁰ is an apocalyptic number.

829440 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 829440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1486485).

829440 is an abundant number, since it is smaller than the sum of its proper divisors (2143530).

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

829440 is an equidigital number, since it uses as much as digits as its factorization.

829440 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 39 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 829440 is about 910.7359661285. The cubic root of 829440 is about 93.9568233881.

Adding to 829440 its product of nonzero digits (2304), we get a square (831744 = 912²).

The spelling of 829440 in words is "eight hundred twenty-nine thousand, four hundred forty".