100512813416400 has 2400 divisors, whose sum is σ = 456432500736000. Its totient is φ = 20575513728000.

The previous prime is 100512813416399. The next prime is 100512813416443. The reversal of 100512813416400 is 4614318215001.

100512813416400 is a `hidden beast` number, since 1 + 0 + 0 + 5 + 1 + 2 + 8 + 1 + 3 + 4 + 1 + 640 + 0 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 479 ways as a sum of consecutive naturals, for example, 78587030961 + ... + 78587032239.

It is an arithmetic number, because the mean of its divisors is an integer number (190180208640).

Almost surely, 2^{100512813416400} is an apocalyptic number.

100512813416400 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 100512813416400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (228216250368000).

100512813416400 is an abundant number, since it is smaller than the sum of its proper divisors (355919687319600).

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

100512813416400 is a wasteful number, since it uses less digits than its factorization.

100512813416400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1428 (or 1378 counting only the distinct ones).

The product of its (nonzero) digits is 23040, while the sum is 36.

The spelling of 100512813416400 in words is "one hundred trillion, five hundred twelve billion, eight hundred thirteen million, four hundred sixteen thousand, four hundred".