314004960 has 288 divisors, whose sum is σ = 1154829312. Its totient is φ = 77414400.

The previous prime is 314004949. The next prime is 314004961. The reversal of 314004960 is 69400413.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-3 number, since 3×314004960³ (a number of 26 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (314004961) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2472417 + ... + 2472543.

It is an arithmetic number, because the mean of its divisors is an integer number (4009824).

Almost surely, 2^314004960 is an apocalyptic number.

314004960 is a gapful number since it is divisible by the number (30) 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 314004960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (577414656).

314004960 is an abundant number, since it is smaller than the sum of its proper divisors (840824352).

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

314004960 is a wasteful number, since it uses less digits than its factorization.

314004960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 266 (or 255 counting only the distinct ones).

The product of its (nonzero) digits is 2592, while the sum is 27.

The square root of 314004960 is about 17720.1851006134. The cubic root of 314004960 is about 679.6920173937.

The spelling of 314004960 in words is "three hundred fourteen million, four thousand, nine hundred sixty".