7628800 has 72 divisors (see below), whose sum is σ = 19041750. Its totient is φ = 3031040.

The previous prime is 7628773. The next prime is 7628807. The reversal of 7628800 is 88267.

It can be written as a sum of positive squares in 3 ways, for example, as 4064256 + 3564544 = 2016^2 + 1888^2 .

It is not an unprimeable number, because it can be changed into a prime (7628807) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 51126 + ... + 51274.

Almost surely, 2^7628800 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 7628800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (9520875).

7628800 is an abundant number, since it is smaller than the sum of its proper divisors (11412950).

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

7628800 is a wasteful number, since it uses less digits than its factorization.

7628800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 181 (or 156 counting only the distinct ones).

The product of its (nonzero) digits is 5376, while the sum is 31.

The square root of 7628800 is about 2762.0282402611. The cubic root of 7628800 is about 196.8575503137.

The spelling of 7628800 in words is "seven million, six hundred twenty-eight thousand, eight hundred".