314216456400 has 360 divisors, whose sum is σ = 1359483862464. Its totient is φ = 65291673600.

The previous prime is 314216456377. The next prime is 314216456423. The reversal of 314216456400 is 4654612413.

314216456400 is a `hidden beast` number, since 3 + 1 + 4 + 2 + 1 + 6 + 4 + 5 + 640 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (314216456377) and next prime (314216456423).

It is a tau number, because it is divible by the number of its divisors (360).

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

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 289569 + ... + 843968.

Almost surely, 2^314216456400 is an apocalyptic number.

314216456400 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 314216456400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (679741931232).

314216456400 is an abundant number, since it is smaller than the sum of its proper divisors (1045267406064).

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

314216456400 is a wasteful number, since it uses less digits than its factorization.

314216456400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1133579 (or 1133565 counting only the distinct ones).

The product of its (nonzero) digits is 69120, while the sum is 36.

The spelling of 314216456400 in words is "three hundred fourteen billion, two hundred sixteen million, four hundred fifty-six thousand, four hundred".