829438128 has 120 divisors (see below), whose sum is σ = 2381633280. Its totient is φ = 269368320.

The previous prime is 829438123. The next prime is 829438133. The reversal of 829438128 is 821834928.

It is an interprime number because it is at equal distance from previous prime (829438123) and next prime (829438133).

It is a super-3 number, since 3×829438128³ (a number of 28 digits) contains 333 as substring.

It is a nude number because it is divisible by every one of its digits.

It is not an unprimeable number, because it can be changed into a prime (829438123) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1457428 + ... + 1457996.

It is an arithmetic number, because the mean of its divisors is an integer number (19846944).

Almost surely, 2^829438128 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 829438128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1190816640).

829438128 is an abundant number, since it is smaller than the sum of its proper divisors (1552195152).

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

829438128 is a wasteful number, since it uses less digits than its factorization.

829438128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 827 (or 818 counting only the distinct ones).

The product of its digits is 221184, while the sum is 45.

The square root of 829438128 is about 28799.9674999817. The cubic root of 829438128 is about 939.5675270289.

The spelling of 829438128 in words is "eight hundred twenty-nine million, four hundred thirty-eight thousand, one hundred twenty-eight".