9963972000 has 768 divisors, whose sum is σ = 39456668160. Its totient is φ = 2463436800.

The previous prime is 9963971993. The next prime is 9963972013. The reversal of 9963972000 is 2793699.

9963972000 is a `hidden beast` number, since 9 + 9 + 639 + 7 + 2 + 0 + 0 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is an unprimeable number.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 148715967 + ... + 148716033.

It is an arithmetic number, because the mean of its divisors is an integer number (51375870).

Almost surely, 2^9963972000 is an apocalyptic number.

9963972000 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 9963972000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (19728334080).

9963972000 is an abundant number, since it is smaller than the sum of its proper divisors (29492696160).

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

9963972000 is an equidigital number, since it uses as much as digits as its factorization.

9963972000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 130 (or 94 counting only the distinct ones).

The product of its (nonzero) digits is 183708, while the sum is 45.

The square root of 9963972000 is about 99819.6974549613. The cubic root of 9963972000 is about 2151.8442441501.

The spelling of 9963972000 in words is "nine billion, nine hundred sixty-three million, nine hundred seventy-two thousand".