9729849600 has 405 divisors, whose sum is σ = 36240200227. Its totient is φ = 2575687680.

The previous prime is 9729849557. The next prime is 9729849607. The reversal of 9729849600 is 69489279.

The square root of 9729849600 is 98640.

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

9729849600 is a `hidden beast` number, since 9 + 7 + 29 + 8 + 4 + 9 + 600 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 28387584 + 9701462016 = 5328^2 + 98496^2 .

It is a tau number, because it is divible by the number of its divisors (405).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (9729849607) by changing a digit.

It is a polite number, since it can be written in 44 ways as a sum of consecutive naturals, for example, 71020732 + ... + 71020868.

Almost surely, 2^9729849600 is an apocalyptic number.

9729849600 is a gapful number since it is divisible by the number (90) formed by its first and last digit.

9729849600 is the 98640-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 9729849600

9729849600 is an abundant number, since it is smaller than the sum of its proper divisors (26510350627).

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

9729849600 is an equidigital number, since it uses as much as digits as its factorization.

9729849600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 312 (or 147 counting only the distinct ones).

The product of its (nonzero) digits is 1959552, while the sum is 54.

The cubic root of 9729849600 is about 2134.8566030490.

It can be divided in two parts, 9729 and 849600, that added together give a square (859329 = 927²).

The spelling of 9729849600 in words is "nine billion, seven hundred twenty-nine million, eight hundred forty-nine thousand, six hundred".