10517978400 has 144 divisors (see below), whose sum is σ = 34575787008. Its totient is φ = 2776960000.

The previous prime is 10517978389. The next prime is 10517978413. The reversal of 10517978400 is 487971501.

10517978400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a super-2 number, since 2×10517978400² (a number of 21 digits) contains 22 as substring.

It is an unprimeable number.

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, 220705 + ... + 264095.

It is an arithmetic number, because the mean of its divisors is an integer number (240109632).

Almost surely, 2^10517978400 is an apocalyptic number.

10517978400 is a gapful number since it is divisible by the number (10) 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 10517978400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (17287893504).

10517978400 is an abundant number, since it is smaller than the sum of its proper divisors (24057808608).

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

10517978400 is a wasteful number, since it uses less digits than its factorization.

10517978400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 43515 (or 43502 counting only the distinct ones).

The product of its (nonzero) digits is 70560, while the sum is 42.

The spelling of 10517978400 in words is "ten billion, five hundred seventeen million, nine hundred seventy-eight thousand, four hundred".