7984656000 has 640 divisors, whose sum is σ = 30439815120. Its totient is φ = 2073600000.

The previous prime is 7984655993. The next prime is 7984656047. The reversal of 7984656000 is 6564897.

7984656000 is a `hidden beast` number, since 7 + 9 + 84 + 6 + 560 + 0 + 0 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 230796864 + 7753859136 = 15192^2 + 88056^2 .

It is a tau number, because it is divible by the number of its divisors (640).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 79055950 + ... + 79056050.

Almost surely, 2^7984656000 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 7984656000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15219907560).

7984656000 is an abundant number, since it is smaller than the sum of its proper divisors (22455159120).

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

7984656000 is a wasteful number, since it uses less digits than its factorization.

7984656000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 203 (or 172 counting only the distinct ones).

The product of its (nonzero) digits is 362880, while the sum is 45.

The square root of 7984656000 is about 89356.9023634996. The cubic root of 7984656000 is about 1998.7205149669.

The spelling of 7984656000 in words is "seven billion, nine hundred eighty-four million, six hundred fifty-six thousand".