101009118400 has 168 divisors, whose sum is σ = 259743732480. Its totient is φ = 38588605440.

The previous prime is 101009118361. The next prime is 101009118437. The reversal of 101009118400 is 4811900101.

101009118400 = 28028² + 28029² + ... + 28155².

It is a Harshad number since it is a multiple of its sum of digits (25).

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 30431941 + ... + 30435259.

Almost surely, 2^101009118400 is an apocalyptic number.

101009118400 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 101009118400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (129871866240).

101009118400 is an abundant number, since it is smaller than the sum of its proper divisors (158734614080).

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

101009118400 is a wasteful number, since it uses less digits than its factorization.

101009118400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4191 (or 4176 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 25.

The spelling of 101009118400 in words is "one hundred one billion, nine million, one hundred eighteen thousand, four hundred".