829716400 has 60 divisors (see below), whose sum is σ = 2009212672. Its totient is φ = 329253120.

The previous prime is 829716367. The next prime is 829716451. The reversal of 829716400 is 4617928.

It is a self number, because there is not a number n which added to its sum of digits gives 829716400.

It is an unprimeable number.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 42634 + ... + 58966.

Almost surely, 2^829716400 is an apocalyptic number.

829716400 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 829716400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1004606336).

829716400 is an abundant number, since it is smaller than the sum of its proper divisors (1179496272).

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

829716400 is a wasteful number, since it uses less digits than its factorization.

829716400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 16478 (or 16467 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 37.

The square root of 829716400 is about 28804.7982114092. The cubic root of 829716400 is about 939.6725885529.

It can be divided in two parts, 829716 and 400, that added together give a triangular number (830116 = T₁₂₈₈).

The spelling of 829716400 in words is "eight hundred twenty-nine million, seven hundred sixteen thousand, four hundred".