7665638400 has 792 divisors, whose sum is σ = 32337687200. Its totient is φ = 1734082560.

The previous prime is 7665638399. The next prime is 7665638437. The reversal of 7665638400 is 48365667.

7665638400 is a `hidden beast` number, since 7 + 6 + 6 + 5 + 638 + 4 + 0 + 0 = 666.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 79027152 + ... + 79027248.

Almost surely, 2^7665638400 is an apocalyptic number.

7665638400 is a gapful number since it is divisible by the number (70) 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 7665638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (16168843600).

7665638400 is an abundant number, since it is smaller than the sum of its proper divisors (24672048800).

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

7665638400 is a wasteful number, since it uses less digits than its factorization.

7665638400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 154 (or 114 counting only the distinct ones).

The product of its (nonzero) digits is 725760, while the sum is 45.

The square root of 7665638400 is about 87553.6315637450. The cubic root of 7665638400 is about 1971.7390743262.

The spelling of 7665638400 in words is "seven billion, six hundred sixty-five million, six hundred thirty-eight thousand, four hundred".