100509771264000 has 832 divisors, whose sum is σ = 383844193873920. Its totient is φ = 22876952985600.

The previous prime is 100509771263977. The next prime is 100509771264017. The reversal of 100509771264000 is 462177905001.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (42).

It is a congruent number.

It is an unprimeable number.

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 63 ways as a sum of consecutive naturals, for example, 2569708444 + ... + 2569747556.

It is an arithmetic number, because the mean of its divisors is an integer number (461351194560).

Almost surely, 2^{100509771264000} is an apocalyptic number.

100509771264000 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 100509771264000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (191922096936960).

100509771264000 is an abundant number, since it is smaller than the sum of its proper divisors (283334422609920).

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

100509771264000 is an equidigital number, since it uses as much as digits as its factorization.

100509771264000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 39401 (or 39369 counting only the distinct ones).

The product of its (nonzero) digits is 105840, while the sum is 42.

The spelling of 100509771264000 in words is "one hundred trillion, five hundred nine billion, seven hundred seventy-one million, two hundred sixty-four thousand".