4417768000 has 112 divisors (see below), whose sum is σ = 11055333744. Its totient is φ = 1748582400.

The previous prime is 4417767997. The next prime is 4417768007. The reversal of 4417768000 is 8677144.

It can be written as a sum of positive squares in 8 ways, for example, as 2470487616 + 1947280384 = 49704^2 + 44128^2 .

It is not an unprimeable number, because it can be changed into a prime (4417768007) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 773154 + ... + 778846.

It is an arithmetic number, because the mean of its divisors is an integer number (98708337).

Almost surely, 2^4417768000 is an apocalyptic number.

4417768000 is a gapful number since it is divisible by the number (40) 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 4417768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (5527666872).

4417768000 is an abundant number, since it is smaller than the sum of its proper divisors (6637565744).

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

4417768000 is an equidigital number, since it uses as much as digits as its factorization.

4417768000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 5817 (or 5797 counting only the distinct ones).

The product of its (nonzero) digits is 37632, while the sum is 37.

The square root of 4417768000 is about 66466.2922089084. The cubic root of 4417768000 is about 1640.8452909941.

The spelling of 4417768000 in words is "four billion, four hundred seventeen million, seven hundred sixty-eight thousand".