9965629600 has 144 divisors (see below), whose sum is σ = 25422669720. Its totient is φ = 3809792000.

The previous prime is 9965629579. The next prime is 9965629601. The reversal of 9965629600 is 69265699.

9965629600 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 12 ways, for example, as 1026305296 + 8939324304 = 32036^2 + 94548^2 .

It is not an unprimeable number, because it can be changed into a prime (9965629601) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2341074 + ... + 2345326.

Almost surely, 2^9965629600 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 9965629600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (12711334860).

9965629600 is an abundant number, since it is smaller than the sum of its proper divisors (15457040120).

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

9965629600 is a wasteful number, since it uses less digits than its factorization.

9965629600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 4403 (or 4390 counting only the distinct ones).

The product of its (nonzero) digits is 1574640, while the sum is 52.

The square root of 9965629600 is about 99828.0000801378. Note that the first 4 decimals coincide. The cubic root of 9965629600 is about 2151.9635640105.

The spelling of 9965629600 in words is "nine billion, nine hundred sixty-five million, six hundred twenty-nine thousand, six hundred".