9735768900 has 729 divisors, whose sum is σ = 37969156407. Its totient is φ = 2083910400.

The previous prime is 9735768883. The next prime is 9735768949. The reversal of 9735768900 is 98675379.

The square root of 9735768900 is 98670.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 4 ways, for example, as 2509408836 + 7226360064 = 50094^2 + 85008^2 .

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 242 ways as a sum of consecutive naturals, for example, 423294289 + ... + 423294311.

Almost surely, 2^9735768900 is an apocalyptic number.

9735768900 is a gapful number since it is divisible by the number (90) formed by its first and last digit.

9735768900 is the 98670-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 9735768900

9735768900 is an abundant number, since it is smaller than the sum of its proper divisors (28233387507).

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

9735768900 is a wasteful number, since it uses less digits than its factorization.

9735768900 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 114 (or 57 counting only the distinct ones).

The product of its (nonzero) digits is 2857680, while the sum is 54.

The cubic root of 9735768900 is about 2135.2894393027.

The spelling of 9735768900 in words is "nine billion, seven hundred thirty-five million, seven hundred sixty-eight thousand, nine hundred".