10072508846400 has 2688 divisors, whose sum is σ = 49636889702400. Its totient is φ = 1918793318400.

The previous prime is 10072508846357. The next prime is 10072508846401. The reversal of 10072508846400 is 464880527001.

10072508846400 is a `hidden beast` number, since 1 + 0 + 0 + 7 + 2 + 508 + 84 + 64 + 0 + 0 = 666.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (10072508846401) by changing a digit.

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 383 ways as a sum of consecutive naturals, for example, 7048640886 + ... + 7048642314.

It is an arithmetic number, because the mean of its divisors is an integer number (18466104800).

Almost surely, 2^{10072508846400} is an apocalyptic number.

10072508846400 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 10072508846400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (24818444851200).

10072508846400 is an abundant number, since it is smaller than the sum of its proper divisors (39564380856000).

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

10072508846400 is a wasteful number, since it uses less digits than its factorization.

10072508846400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1654 (or 1633 counting only the distinct ones).

The product of its (nonzero) digits is 430080, while the sum is 45.

The spelling of 10072508846400 in words is "ten trillion, seventy-two billion, five hundred eight million, eight hundred forty-six thousand, four hundred".