329814144 has 192 divisors, whose sum is σ = 1096973280. Its totient is φ = 94003200.

The previous prime is 329814119. The next prime is 329814157. The reversal of 329814144 is 441418923.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (192).

It is a Harshad number since it is a multiple of its sum of digits (36).

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

It is a junction number, because it is equal to n+sod(n) for n = 329814099 and 329814108.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 214659 + ... + 216189.

Almost surely, 2^329814144 is an apocalyptic number.

329814144 is a gapful number since it is divisible by the number (34) 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 329814144, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (548486640).

329814144 is an abundant number, since it is smaller than the sum of its proper divisors (767159136).

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

329814144 is a wasteful number, since it uses less digits than its factorization.

329814144 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1579 (or 1564 counting only the distinct ones).

The product of its digits is 27648, while the sum is 36.

The square root of 329814144 is about 18160.7858860788. The cubic root of 329814144 is about 690.9125669598.

The spelling of 329814144 in words is "three hundred twenty-nine million, eight hundred fourteen thousand, one hundred forty-four".