972820800 has 336 divisors, whose sum is σ = 4054165120. Its totient is φ = 222289920.

The previous prime is 972820799. The next prime is 972820813. The reversal of 972820800 is 8028279.

It is a tau number, because it is divible by the number of its divisors (336).

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 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, 300792 + ... + 304008.

Almost surely, 2^972820800 is an apocalyptic number.

972820800 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 972820800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2027082560).

972820800 is an abundant number, since it is smaller than the sum of its proper divisors (3081344320).

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

972820800 is a wasteful number, since it uses less digits than its factorization.

972820800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3255 (or 3234 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 36.

The square root of 972820800 is about 31190.0753445707. The cubic root of 972820800 is about 990.8569256320.

The spelling of 972820800 in words is "nine hundred seventy-two million, eight hundred twenty thousand, eight hundred".