512314000 has 240 divisors, whose sum is σ = 1427877360. Its totient is φ = 177408000.

The previous prime is 512313979. The next prime is 512314003. The reversal of 512314000 is 413215.

It can be written as a sum of positive squares in 8 ways, for example, as 144288144 + 368025856 = 12012^2 + 19184^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is not an unprimeable number, because it can be changed into a prime (512314003) 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, 7017964 + ... + 7018036.

It is an arithmetic number, because the mean of its divisors is an integer number (5949489).

Almost surely, 2^512314000 is an apocalyptic number.

512314000 is a gapful number since it is divisible by the number (50) 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 512314000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (713938680).

512314000 is an abundant number, since it is smaller than the sum of its proper divisors (915563360).

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

512314000 is a wasteful number, since it uses less digits than its factorization.

512314000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 147 (or 120 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 16.

The square root of 512314000 is about 22634.3544197753. The cubic root of 512314000 is about 800.1635082457.

Adding to 512314000 its reverse (413215), we get a palindrome (512727215).

The spelling of 512314000 in words is "five hundred twelve million, three hundred fourteen thousand".