712416000 has 288 divisors, whose sum is σ = 2437396416. Its totient is φ = 184320000.

The previous prime is 712415981. The next prime is 712416013. The reversal of 712416000 is 614217.

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 31 ways as a sum of consecutive naturals, for example, 3935910 + ... + 3936090.

It is an arithmetic number, because the mean of its divisors is an integer number (8463182).

Almost surely, 2^712416000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 712416000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1218698208).

712416000 is an abundant number, since it is smaller than the sum of its proper divisors (1724980416).

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

712416000 is a wasteful number, since it uses less digits than its factorization.

712416000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 256 (or 232 counting only the distinct ones).

The product of its (nonzero) digits is 336, while the sum is 21.

The square root of 712416000 is about 26691.1221195363. The cubic root of 712416000 is about 893.1228929324.

The spelling of 712416000 in words is "seven hundred twelve million, four hundred sixteen thousand".