638928000 has 640 divisors, whose sum is σ = 2599225200. Its totient is φ = 154828800.

The previous prime is 638927981. The next prime is 638928007. The reversal of 638928000 is 829836.

It can be written as a sum of positive squares in 8 ways, for example, as 70963776 + 567964224 = 8424^2 + 23832^2 .

It is a tau number, because it is divible by the number of its divisors (640).

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

It is not an unprimeable number, because it can be changed into a prime (638928007) by changing a digit.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 22031986 + ... + 22032014.

Almost surely, 2^638928000 is an apocalyptic number.

638928000 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 638928000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1299612600).

638928000 is an abundant number, since it is smaller than the sum of its proper divisors (1960297200).

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

638928000 is a wasteful number, since it uses less digits than its factorization.

638928000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 56 counting only the distinct ones).

The product of its (nonzero) digits is 20736, while the sum is 36.

The square root of 638928000 is about 25277.0251414204. The cubic root of 638928000 is about 861.2924500357.

The spelling of 638928000 in words is "six hundred thirty-eight million, nine hundred twenty-eight thousand".