9768000 has 224 divisors, whose sum is σ = 36137088. Its totient is φ = 2304000.

The previous prime is 9767999. The next prime is 9768001. The reversal of 9768000 is 8679.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (9767999) and next prime (9768001).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is not an unprimeable number, because it can be changed into a prime (9768001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 263982 + ... + 264018.

Almost surely, 2^9768000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 9768000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (18068544).

9768000 is an abundant number, since it is smaller than the sum of its proper divisors (26369088).

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

9768000 is a wasteful number, since it uses less digits than its factorization.

9768000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 78 (or 58 counting only the distinct ones).

The product of its (nonzero) digits is 3024, while the sum is 30.

The square root of 9768000 is about 3125.3799768988. The cubic root of 9768000 is about 213.7643196863.

The spelling of 9768000 in words is "nine million, seven hundred sixty-eight thousand".