72205200 has 180 divisors, whose sum is σ = 259054848. Its totient is φ = 18604800.

The previous prime is 72205193. The next prime is 72205201. The reversal of 72205200 is 250227.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (180).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is not an unprimeable number, because it can be changed into a prime (72205201) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 111277 + ... + 111923.

Almost surely, 2^72205200 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 72205200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (129527424).

72205200 is an abundant number, since it is smaller than the sum of its proper divisors (186849648).

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

72205200 is a wasteful number, since it uses less digits than its factorization.

72205200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 702 (or 688 counting only the distinct ones).

The product of its (nonzero) digits is 280, while the sum is 18.

The square root of 72205200 is about 8497.3642972395. The cubic root of 72205200 is about 416.4116056750.

Adding to 72205200 its reverse (250227), we get a palindrome (72455427).

The spelling of 72205200 in words is "seventy-two million, two hundred five thousand, two hundred".