972345600 has 432 divisors, whose sum is σ = 3786632640. Its totient is φ = 243302400.

The previous prime is 972345593. The next prime is 972345613. The reversal of 972345600 is 6543279.

972345600 is a `hidden beast` number, since 9 + 7 + 2 + 3 + 45 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (432).

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

It is an unprimeable number.

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 47 ways as a sum of consecutive naturals, for example, 2937435 + ... + 2937765.

Almost surely, 2^972345600 is an apocalyptic number.

972345600 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 972345600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1893316320).

972345600 is an abundant number, since it is smaller than the sum of its proper divisors (2814287040).

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

972345600 is a wasteful number, since it uses less digits than its factorization.

972345600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 383 (or 358 counting only the distinct ones).

The product of its (nonzero) digits is 45360, while the sum is 36.

The square root of 972345600 is about 31182.4566062393. The cubic root of 972345600 is about 990.6955626146.

Adding to 972345600 its reverse (6543279), we get a palindrome (978888879).

The spelling of 972345600 in words is "nine hundred seventy-two million, three hundred forty-five thousand, six hundred".