972129600 has 420 divisors, whose sum is σ = 3854842684. Its totient is φ = 238878720.

The previous prime is 972129593. The next prime is 972129617. The reversal of 972129600 is 6921279.

972129600 is a `hidden beast` number, since 9 + 7 + 21 + 29 + 600 = 666.

It can be written as a sum of positive squares in 6 ways, for example, as 186624 + 971942976 = 432^2 + 31176^2 .

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 59 ways as a sum of consecutive naturals, for example, 1684512 + ... + 1685088.

Almost surely, 2^972129600 is an apocalyptic number.

972129600 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 972129600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1927421342).

972129600 is an abundant number, since it is smaller than the sum of its proper divisors (2882713084).

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

972129600 is a wasteful number, since it uses less digits than its factorization.

972129600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 624 (or 600 counting only the distinct ones).

The product of its (nonzero) digits is 13608, while the sum is 36.

The square root of 972129600 is about 31178.9929279315. The cubic root of 972129600 is about 990.6221984085.

The spelling of 972129600 in words is "nine hundred seventy-two million, one hundred twenty-nine thousand, six hundred".