829870272000 has 2880 divisors, whose sum is σ = 3968264139840. Its totient is φ = 172440576000.

The previous prime is 829870271987. The next prime is 829870272037. The reversal of 829870272000 is 272078928.

It is a happy number.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a tau number, because it is divible by the number of its divisors (2880).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 75442751995 + ... + 75442752005.

It is an arithmetic number, because the mean of its divisors is an integer number (1377869493).

Almost surely, 2^829870272000 is an apocalyptic number.

829870272000 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 829870272000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1984132069920).

829870272000 is an abundant number, since it is smaller than the sum of its proper divisors (3138393867840).

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

829870272000 is an frugal number, since it uses more digits than its factorization.

829870272000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 90 (or 28 counting only the distinct ones).

The product of its (nonzero) digits is 225792, while the sum is 45.

It can be divided in two parts, 829870 and 272000, that added together give a triangular number (1101870 = T₁₄₈₄).

The spelling of 829870272000 in words is "eight hundred twenty-nine billion, eight hundred seventy million, two hundred seventy-two thousand".