10127415916800 has 3456 divisors, whose sum is σ = 47581274603520. Its totient is φ = 2051171942400.

The previous prime is 10127415916777. The next prime is 10127415916801. The reversal of 10127415916800 is 861951472101.

10127415916800 is a `hidden beast` number, since 1 + 0 + 12 + 7 + 41 + 591 + 6 + 8 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (3456).

It is a Harshad number since it is a multiple of its sum of digits (45).

It is not an unprimeable number, because it can be changed into a prime (10127415916801) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 52473657504 + ... + 52473657696.

It is an arithmetic number, because the mean of its divisors is an integer number (13767729920).

Almost surely, 2^{10127415916800} is an apocalyptic number.

10127415916800 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 10127415916800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (23790637301760).

10127415916800 is an abundant number, since it is smaller than the sum of its proper divisors (37453858686720).

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

10127415916800 is a wasteful number, since it uses less digits than its factorization.

10127415916800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 366 (or 341 counting only the distinct ones).

The product of its (nonzero) digits is 120960, while the sum is 45.

The spelling of 10127415916800 in words is "ten trillion, one hundred twenty-seven billion, four hundred fifteen million, nine hundred sixteen thousand, eight hundred".