972564480000 has 900 divisors, whose sum is σ = 3588987990588. Its totient is φ = 253624320000.

The previous prime is 972564479993. The next prime is 972564480007. The reversal of 972564480000 is 84465279.

It is a happy number.

972564480000 is a `hidden beast` number, since 9 + 7 + 2 + 564 + 4 + 80 + 0 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (972564479993) and next prime (972564480007).

It can be written as a sum of positive squares in 10 ways, for example, as 796406317056 + 176158162944 = 892416^2 + 419712^2 .

It is a tau number, because it is divible by the number of its divisors (900).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (972564480007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 5621759914 + ... + 5621760086.

Almost surely, 2^972564480000 is an apocalyptic number.

972564480000 is a gapful number since it is divisible by the number (90) 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 972564480000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1794493995294).

972564480000 is an abundant number, since it is smaller than the sum of its proper divisors (2616423510588).

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

972564480000 is an equidigital number, since it uses as much as digits as its factorization.

972564480000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 288 (or 244 counting only the distinct ones).

The product of its (nonzero) digits is 483840, while the sum is 45.

The spelling of 972564480000 in words is "nine hundred seventy-two billion, five hundred sixty-four million, four hundred eighty thousand".