72105600 has 384 divisors, whose sum is σ = 288374400. Its totient is φ = 15482880.

The previous prime is 72105587. The next prime is 72105613. The reversal of 72105600 is 650127.

It is an interprime number because it is at equal distance from previous prime (72105587) and next prime (72105613).

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1948782 + ... + 1948818.

It is an arithmetic number, because the mean of its divisors is an integer number (750975).

Almost surely, 2^72105600 is an apocalyptic number.

72105600 is a gapful number since it is divisible by the number (70) 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 72105600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (144187200).

72105600 is an abundant number, since it is smaller than the sum of its proper divisors (216268800).

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

72105600 is a wasteful number, since it uses less digits than its factorization.

72105600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 100 (or 83 counting only the distinct ones).

The product of its (nonzero) digits is 420, while the sum is 21.

The square root of 72105600 is about 8491.5016339868. The cubic root of 72105600 is about 416.2200512320.

Adding to 72105600 its reverse (650127), we get a palindrome (72755727).

The spelling of 72105600 in words is "seventy-two million, one hundred five thousand, six hundred".