312120000 has 420 divisors, whose sum is σ = 1218016360. Its totient is φ = 78336000.

The previous prime is 312119993. The next prime is 312120013. The reversal of 312120000 is 21213.

It is a happy number.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a nialpdrome in base 12.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 18359992 + ... + 18360008.

Almost surely, 2^312120000 is an apocalyptic number.

312120000 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 312120000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (609008180).

312120000 is an abundant number, since it is smaller than the sum of its proper divisors (905896360).

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

312120000 is an equidigital number, since it uses as much as digits as its factorization.

312120000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 12, while the sum is 9.

The square root of 312120000 is about 17666.9182372025. The cubic root of 312120000 is about 678.3292315968.

Multiplying 312120000 by its product of nonzero digits (12), we get a square (3745440000 = 61200²).

312120000 divided by its product of nonzero digits (12) gives a square (26010000 = 5100²).

Adding to 312120000 its reverse (21213), we get a palindrome (312141213).

The spelling of 312120000 in words is "three hundred twelve million, one hundred twenty thousand".