314240400 has 180 divisors, whose sum is σ = 1117623780. Its totient is φ = 81715200.

The previous prime is 314240387. The next prime is 314240417. The reversal of 314240400 is 4042413.

It can be written as a sum of positive squares in 6 ways, for example, as 86713344 + 227527056 = 9312^2 + 15084^2 .

It is a tau number, because it is divible by the number of its divisors (180).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 146536 + ... + 148664.

It is an arithmetic number, because the mean of its divisors is an integer number (6209021).

Almost surely, 2^314240400 is an apocalyptic number.

314240400 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 314240400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (558811890).

314240400 is an abundant number, since it is smaller than the sum of its proper divisors (803383380).

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

314240400 is a wasteful number, since it uses less digits than its factorization.

314240400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2194 (or 2180 counting only the distinct ones).

The product of its (nonzero) digits is 384, while the sum is 18.

The square root of 314240400 is about 17726.8271272667. The cubic root of 314240400 is about 679.8618519820.

Adding to 314240400 its reverse (4042413), we get a palindrome (318282813).

The spelling of 314240400 in words is "three hundred fourteen million, two hundred forty thousand, four hundred".