9760640400 has 960 divisors, whose sum is σ = 42157301760. Its totient is φ = 2098483200.

The previous prime is 9760640371. The next prime is 9760640429. The reversal of 9760640400 is 40460679.

9760640400 is a `hidden beast` number, since 9 + 7 + 6 + 0 + 640 + 4 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (9760640371) and next prime (9760640429).

It is a super-2 number, since 2×9760640400² (a number of 21 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 145681167 + ... + 145681233.

It is an arithmetic number, because the mean of its divisors is an integer number (43913856).

Almost surely, 2^9760640400 is an apocalyptic number.

9760640400 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 9760640400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (21078650880).

9760640400 is an abundant number, since it is smaller than the sum of its proper divisors (32396661360).

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

9760640400 is a wasteful number, since it uses less digits than its factorization.

9760640400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 189 (or 172 counting only the distinct ones).

The product of its (nonzero) digits is 36288, while the sum is 36.

The square root of 9760640400 is about 98795.9533584246. The cubic root of 9760640400 is about 2137.1062001525.

The spelling of 9760640400 in words is "nine billion, seven hundred sixty million, six hundred forty thousand, four hundred".