972817200 has 360 divisors, whose sum is σ = 3645957120. Its totient is φ = 239500800.

The previous prime is 972817189. The next prime is 972817201. The reversal of 972817200 is 2718279.

It is a tau number, because it is divible by the number of its divisors (360).

It is a super-3 number, since 3×972817200³ (a number of 28 digits) contains 333 as substring.

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

It is a zygodrome in base 2.

It is not an unprimeable number, because it can be changed into a prime (972817201) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 2566611 + ... + 2566989.

Almost surely, 2^972817200 is an apocalyptic number.

972817200 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 972817200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1822978560).

972817200 is an abundant number, since it is smaller than the sum of its proper divisors (2673139920).

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

972817200 is a wasteful number, since it uses less digits than its factorization.

972817200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 457 (or 443 counting only the distinct ones).

The product of its (nonzero) digits is 14112, while the sum is 36.

The square root of 972817200 is about 31190.0176338520. The cubic root of 972817200 is about 990.8557033825.

The spelling of 972817200 in words is "nine hundred seventy-two million, eight hundred seventeen thousand, two hundred".