72244800 has 252 divisors, whose sum is σ = 267164820. Its totient is φ = 18493440.

The previous prime is 72244769. The next prime is 72244813. The reversal of 72244800 is 844227.

It can be written as a sum of positive squares in 6 ways, for example, as 876096 + 71368704 = 936^2 + 8448^2 .

It is a super-2 number, since 2×72244800² = 10438622254080000, which contains 22 as substring.

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 35 ways as a sum of consecutive naturals, for example, 417514 + ... + 417686.

Almost surely, 2^72244800 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 72244800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (133582410).

72244800 is an abundant number, since it is smaller than the sum of its proper divisors (194920020).

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

72244800 is a wasteful number, since it uses less digits than its factorization.

72244800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 230 (or 212 counting only the distinct ones).

The product of its (nonzero) digits is 3584, while the sum is 27.

The square root of 72244800 is about 8499.6941121431. The cubic root of 72244800 is about 416.4877169336.

The spelling of 72244800 in words is "seventy-two million, two hundred forty-four thousand, eight hundred".