968584000 has 112 divisors (see below), whose sum is σ = 2458035216. Its totient is φ = 377856000.

The previous prime is 968583991. The next prime is 968584051. The reversal of 968584000 is 485869.

It can be written as a sum of positive squares in 8 ways, for example, as 418775296 + 549808704 = 20464^2 + 23448^2 .

It is a Harshad number since it is a multiple of its sum of digits (40).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 326524 + ... + 329476.

It is an arithmetic number, because the mean of its divisors is an integer number (21946743).

Almost surely, 2^968584000 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 968584000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1229017608).

968584000 is an abundant number, since it is smaller than the sum of its proper divisors (1489451216).

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

968584000 is a wasteful number, since it uses less digits than its factorization.

968584000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3021 (or 3001 counting only the distinct ones).

The product of its (nonzero) digits is 69120, while the sum is 40.

The square root of 968584000 is about 31122.0821925526. The cubic root of 968584000 is about 989.4163822018.

The spelling of 968584000 in words is "nine hundred sixty-eight million, five hundred eighty-four thousand".