72755200 has 216 divisors, whose sum is σ = 217075950. Its totient is φ = 24084480.

The previous prime is 72755153. The next prime is 72755203. The reversal of 72755200 is 255727.

It can be written as a sum of positive squares in 3 ways, for example, as 54641664 + 18113536 = 7392^2 + 4256^2 .

It is a Harshad number since it is a multiple of its sum of digits (28).

It is not an unprimeable number, because it can be changed into a prime (72755203) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 2508786 + ... + 2508814.

Almost surely, 2^72755200 is an apocalyptic number.

72755200 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 72755200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (108537975).

72755200 is an abundant number, since it is smaller than the sum of its proper divisors (144320750).

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

72755200 is a wasteful number, since it uses less digits than its factorization.

72755200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75 (or 43 counting only the distinct ones).

The product of its (nonzero) digits is 4900, while the sum is 28.

The square root of 72755200 is about 8529.6658785676. The cubic root of 72755200 is about 417.4662264862.

The spelling of 72755200 in words is "seventy-two million, seven hundred fifty-five thousand, two hundred".