668188800 has 144 divisors (see below), whose sum is σ = 2384353530. Its totient is φ = 178176000.

The previous prime is 668188793. The next prime is 668188813. The reversal of 668188800 is 8881866.

It is a happy number.

It can be written as a sum of positive squares in 3 ways, for example, as 619412544 + 48776256 = 24888^2 + 6984^2 .

It is a tau number, because it is divible by the number of its divisors (144).

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

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 17200 + ... + 40400.

Almost surely, 2^668188800 is an apocalyptic number.

668188800 is a gapful number since it is divisible by the number (60) 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 668188800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1192176765).

668188800 is an abundant number, since it is smaller than the sum of its proper divisors (1716164730).

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

668188800 is a wasteful number, since it uses less digits than its factorization.

668188800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 23231 (or 23211 counting only the distinct ones).

The product of its (nonzero) digits is 147456, while the sum is 45.

The square root of 668188800 is about 25849.3481542572. The cubic root of 668188800 is about 874.2448123521.

It can be divided in two parts, 6681 and 88800, that added together give a square (95481 = 309²).

The spelling of 668188800 in words is "six hundred sixty-eight million, one hundred eighty-eight thousand, eight hundred".