1007668800 has 504 divisors, whose sum is σ = 3930700800. Its totient is φ = 243855360.

The previous prime is 1007668789. The next prime is 1007668817. The reversal of 1007668800 is 88667001.

It is a Harshad number since it is a multiple of its sum of digits (36).

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, 7934337 + ... + 7934463.

Almost surely, 2^1007668800 is an apocalyptic number.

1007668800 is a gapful number since it is divisible by the number (10) 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 1007668800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1965350400).

1007668800 is an abundant number, since it is smaller than the sum of its proper divisors (2923032000).

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

1007668800 is a wasteful number, since it uses less digits than its factorization.

1007668800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 203 (or 185 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

The square root of 1007668800 is about 31743.7993945274. The cubic root of 1007668800 is about 1002.5497598657.

The spelling of 1007668800 in words is "one billion, seven million, six hundred sixty-eight thousand, eight hundred".