100107878400 has 816 divisors, whose sum is σ = 384866398720. Its totient is φ = 25480396800.

The previous prime is 100107878399. The next prime is 100107878407. The reversal of 100107878400 is 4878701001.

100107878400 is a `hidden beast` number, since 100 + 10 + 78 + 78 + 400 = 666.

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (100107878407) by changing a digit.

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 47 ways as a sum of consecutive naturals, for example, 1371340764 + ... + 1371340836.

Almost surely, 2^100107878400 is an apocalyptic number.

100107878400 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 100107878400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (192433199360).

100107878400 is an abundant number, since it is smaller than the sum of its proper divisors (284758520320).

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

100107878400 is an frugal number, since it uses more digits than its factorization.

100107878400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 155 (or 114 counting only the distinct ones).

The product of its (nonzero) digits is 12544, while the sum is 36.

The spelling of 100107878400 in words is "one hundred billion, one hundred seven million, eight hundred seventy-eight thousand, four hundred".