972518400 has 660 divisors, whose sum is σ = 4176993568. Its totient is φ = 218972160.

The previous prime is 972518389. The next prime is 972518423. The reversal of 972518400 is 4815279.

972518400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 14515167 + ... + 14515233.

Almost surely, 2^972518400 is an apocalyptic number.

972518400 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 972518400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2088496784).

972518400 is an abundant number, since it is smaller than the sum of its proper divisors (3204475168).

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

972518400 is a wasteful number, since it uses less digits than its factorization.

972518400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 116 (or 84 counting only the distinct ones).

The product of its (nonzero) digits is 20160, while the sum is 36.

The square root of 972518400 is about 31185.2272718991. The cubic root of 972518400 is about 990.7542461571.

The spelling of 972518400 in words is "nine hundred seventy-two million, five hundred eighteen thousand, four hundred".