690768000 has 640 divisors, whose sum is σ = 2830267440. Its totient is φ = 165888000.

The previous prime is 690767999. The next prime is 690768031. The reversal of 690768000 is 867096.

It can be written as a sum of positive squares in 8 ways, for example, as 59351616 + 631416384 = 7704^2 + 25128^2 .

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 an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 16847980 + ... + 16848020.

Almost surely, 2^690768000 is an apocalyptic number.

690768000 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 690768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1415133720).

690768000 is an abundant number, since it is smaller than the sum of its proper divisors (2139499440).

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

690768000 is a wasteful number, since it uses less digits than its factorization.

690768000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 95 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 18144, while the sum is 36.

The square root of 690768000 is about 26282.4656377593. The cubic root of 690768000 is about 883.9833197101.

The spelling of 690768000 in words is "six hundred ninety million, seven hundred sixty-eight thousand".