312345600 has 396 divisors, whose sum is σ = 1215328464. Its totient is φ = 70533120.

The previous prime is 312345533. The next prime is 312345637. The reversal of 312345600 is 6543213.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (24).

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, 3763159 + ... + 3763241.

Almost surely, 2^312345600 is an apocalyptic number.

312345600 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 312345600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (607664232).

312345600 is an abundant number, since it is smaller than the sum of its proper divisors (902982864).

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

312345600 is a wasteful number, since it uses less digits than its factorization.

312345600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 130 (or 100 counting only the distinct ones).

The product of its (nonzero) digits is 2160, while the sum is 24.

The square root of 312345600 is about 17673.3018986266. The cubic root of 312345600 is about 678.4926241159.

Adding to 312345600 its reverse (6543213), we get a palindrome (318888813).

The spelling of 312345600 in words is "three hundred twelve million, three hundred forty-five thousand, six hundred".