9972000 has 144 divisors (see below), whose sum is σ = 35518392. Its totient is φ = 2649600.

The previous prime is 9971993. The next prime is 9972007. The reversal of 9972000 is 2799.

It is an interprime number because it is at equal distance from previous prime (9971993) and next prime (9972007).

It can be written as a sum of positive squares in 4 ways, for example, as 1468944 + 8503056 = 1212^2 + 2916^2 .

It is a tau number, because it is divible by the number of its divisors (144).

It is a nialpdrome in base 10.

It is not an unprimeable number, because it can be changed into a prime (9972007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 35862 + ... + 36138.

Almost surely, 2^9972000 is an apocalyptic number.

9972000 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 9972000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17759196).

9972000 is an abundant number, since it is smaller than the sum of its proper divisors (25546392).

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

9972000 is a wasteful number, since it uses less digits than its factorization.

9972000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 308 (or 287 counting only the distinct ones).

The product of its (nonzero) digits is 1134, while the sum is 27.

The square root of 9972000 is about 3157.8473680658. The cubic root of 9972000 is about 215.2422004644.

Adding to 9972000 its reverse (2799), we get a palindrome (9974799).

The spelling of 9972000 in words is "nine million, nine hundred seventy-two thousand".