10123120800 has 720 divisors, whose sum is σ = 40613697432. Its totient is φ = 2438553600.

The previous prime is 10123120771. The next prime is 10123120831. The reversal of 10123120800 is 802132101.

It can be written as a sum of positive squares in 12 ways, for example, as 56610576 + 10066510224 = 7524^2 + 100332^2 .

It is a tau number, because it is divible by the number of its divisors (720).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 51386302 + ... + 51386498.

Almost surely, 2^10123120800 is an apocalyptic number.

10123120800 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 10123120800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (20306848716).

10123120800 is an abundant number, since it is smaller than the sum of its proper divisors (30490576632).

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

10123120800 is a wasteful number, since it uses less digits than its factorization.

10123120800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 303 (or 281 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 18.

Adding to 10123120800 its reverse (802132101), we get a palindrome (10925252901).

The spelling of 10123120800 in words is "ten billion, one hundred twenty-three million, one hundred twenty thousand, eight hundred".