72149200 has 60 divisors (see below), whose sum is σ = 174190860. Its totient is φ = 28718080.

The previous prime is 72149191. The next prime is 72149221. The reversal of 72149200 is 294127.

It can be written as a sum of positive squares in 6 ways, for example, as 22924944 + 49224256 = 4788^2 + 7016^2 .

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

It is a congruent number.

It is an unprimeable number.

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 11 ways as a sum of consecutive naturals, for example, 126516 + ... + 127084.

It is an arithmetic number, because the mean of its divisors is an integer number (2903181).

Almost surely, 2^72149200 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 72149200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (87095430).

72149200 is an abundant number, since it is smaller than the sum of its proper divisors (102041660).

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

72149200 is a wasteful number, since it uses less digits than its factorization.

72149200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 904 (or 893 counting only the distinct ones).

The product of its (nonzero) digits is 1008, while the sum is 25.

The square root of 72149200 is about 8494.0685186782. The cubic root of 72149200 is about 416.3039260757.

The spelling of 72149200 in words is "seventy-two million, one hundred forty-nine thousand, two hundred".