101609510400 has 600 divisors, whose sum is σ = 392506980624. Its totient is φ = 25911705600.

The previous prime is 101609510363. The next prime is 101609510407. The reversal of 101609510400 is 4015906101.

101609510400 is a `hidden beast` number, since 1 + 0 + 1 + 609 + 5 + 10 + 40 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (600).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (101609510407) by changing a digit.

It is a polite number, since it can be written in 59 ways as a sum of consecutive naturals, for example, 23844270 + ... + 23848530.

Almost surely, 2^101609510400 is an apocalyptic number.

101609510400 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 101609510400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (196253490312).

101609510400 is an abundant number, since it is smaller than the sum of its proper divisors (290897470224).

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

101609510400 is an equidigital number, since it uses as much as digits as its factorization.

101609510400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 4324 (or 4294 counting only the distinct ones).

The product of its (nonzero) digits is 1080, while the sum is 27.

The spelling of 101609510400 in words is "one hundred one billion, six hundred nine million, five hundred ten thousand, four hundred".