9705600 has 144 divisors (see below), whose sum is σ = 34734570. Its totient is φ = 2580480.

The previous prime is 9705541. The next prime is 9705601. The reversal of 9705600 is 65079.

It can be written as a sum of positive squares in 3 ways, for example, as 6110784 + 3594816 = 2472^2 + 1896^2 .

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (9705601) by changing a digit.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 28632 + ... + 28968.

Almost surely, 2^9705600 is an apocalyptic number.

9705600 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 9705600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17367285).

9705600 is an abundant number, since it is smaller than the sum of its proper divisors (25028970).

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

9705600 is a wasteful number, since it uses less digits than its factorization.

9705600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 367 (or 347 counting only the distinct ones).

The product of its (nonzero) digits is 1890, while the sum is 27.

The square root of 9705600 is about 3115.3811965793. The cubic root of 9705600 is about 213.3081567511.

It can be divided in two parts, 9 and 705600, that multiplied together give a square (6350400 = 2520²).

The spelling of 9705600 in words is "nine million, seven hundred five thousand, six hundred".