100587340800 has 792 divisors, whose sum is σ = 388507613832. Its totient is φ = 24772608000.

The previous prime is 100587340793. The next prime is 100587340807. The reversal of 100587340800 is 8043785001.

It is an interprime number because it is at equal distance from previous prime (100587340793) and next prime (100587340807).

It can be written as a sum of positive squares in 12 ways, for example, as 75435918336 + 25151422464 = 274656^2 + 158592^2 .

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

It is not an unprimeable number, because it can be changed into a prime (100587340807) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 238924590 + ... + 238925010.

Almost surely, 2^100587340800 is an apocalyptic number.

100587340800 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 100587340800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (194253806916).

100587340800 is an abundant number, since it is smaller than the sum of its proper divisors (287920273032).

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

100587340800 is a wasteful number, since it uses less digits than its factorization.

100587340800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 535 (or 509 counting only the distinct ones).

The product of its (nonzero) digits is 26880, while the sum is 36.

The spelling of 100587340800 in words is "one hundred billion, five hundred eighty-seven million, three hundred forty thousand, eight hundred".