829729440 has 384 divisors, whose sum is σ = 3102624000. Its totient is φ = 206696448.

The previous prime is 829729361. The next prime is 829729441. The reversal of 829729440 is 44927928.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (829729441) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 4635271 + ... + 4635449.

It is an arithmetic number, because the mean of its divisors is an integer number (8079750).

Almost surely, 2^829729440 is an apocalyptic number.

829729440 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 829729440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1551312000).

829729440 is an abundant number, since it is smaller than the sum of its proper divisors (2272894560).

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

829729440 is a wasteful number, since it uses less digits than its factorization.

829729440 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 269 (or 255 counting only the distinct ones).

The product of its (nonzero) digits is 290304, while the sum is 45.

The square root of 829729440 is about 28805.0245616976. The cubic root of 829729440 is about 939.6775112254.

The spelling of 829729440 in words is "eight hundred twenty-nine million, seven hundred twenty-nine thousand, four hundred forty".