7638681600 has 648 divisors, whose sum is σ = 30289330890. Its totient is φ = 1838284800.

The previous prime is 7638681581. The next prime is 7638681613. The reversal of 7638681600 is 61868367.

7638681600 is a `hidden beast` number, since 7 + 6 + 38 + 6 + 8 + 1 + 600 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 5942559744 + 1696121856 = 77088^2 + 41184^2 .

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 (11) of ones.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 55756732 + ... + 55756868.

Almost surely, 2^7638681600 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 7638681600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15144665445).

7638681600 is an abundant number, since it is smaller than the sum of its proper divisors (22650649290).

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

7638681600 is a wasteful number, since it uses less digits than its factorization.

7638681600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 197 (or 158 counting only the distinct ones).

The product of its (nonzero) digits is 290304, while the sum is 45.

The square root of 7638681600 is about 87399.5514862634. The cubic root of 7638681600 is about 1969.4251030170.

The spelling of 7638681600 in words is "seven billion, six hundred thirty-eight million, six hundred eighty-one thousand, six hundred".