972316800 has 864 divisors, whose sum is σ = 4428349380. Its totient is φ = 201277440.

The previous prime is 972316757. The next prime is 972316801. The reversal of 972316800 is 8613279.

It can be written as a sum of positive squares in 6 ways, for example, as 276623424 + 695693376 = 16632^2 + 26376^2 .

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

It is not an unprimeable number, because it can be changed into a prime (972316801) by changing a digit.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 18345574 + ... + 18345626.

Almost surely, 2^972316800 is an apocalyptic number.

972316800 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 972316800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2214174690).

972316800 is an abundant number, since it is smaller than the sum of its proper divisors (3456032580).

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

972316800 is a wasteful number, since it uses less digits than its factorization.

972316800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 110 (or 83 counting only the distinct ones).

The product of its (nonzero) digits is 18144, while the sum is 36.

The square root of 972316800 is about 31181.9948046946. The cubic root of 972316800 is about 990.6857813482.

The spelling of 972316800 in words is "nine hundred seventy-two million, three hundred sixteen thousand, eight hundred".