7813648800 has 720 divisors, whose sum is σ = 31085557272. Its totient is φ = 1902182400.

The previous prime is 7813648781. The next prime is 7813648807. The reversal of 7813648800 is 88463187.

It can be written as a sum of positive squares in 12 ways, for example, as 951845904 + 6861802896 = 30852^2 + 82836^2 .

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×7813648800² (a number of 21 digits) contains 22 as substring.

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

It is not an unprimeable number, because it can be changed into a prime (7813648807) by changing a digit.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 45165514 + ... + 45165686.

Almost surely, 2^7813648800 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 7813648800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15542778636).

7813648800 is an abundant number, since it is smaller than the sum of its proper divisors (23271908472).

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

7813648800 is a wasteful number, since it uses less digits than its factorization.

7813648800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 263 (or 241 counting only the distinct ones).

The product of its (nonzero) digits is 258048, while the sum is 45.

The square root of 7813648800 is about 88394.8460035991. The cubic root of 7813648800 is about 1984.3485691976.

The spelling of 7813648800 in words is "seven billion, eight hundred thirteen million, six hundred forty-eight thousand, eight hundred".