72835200 has 240 divisors, whose sum is σ = 269734410. Its totient is φ = 19353600.

The previous prime is 72835199. The next prime is 72835207. The reversal of 72835200 is 253827.

It can be written as a sum of positive squares in 3 ways, for example, as 59351616 + 13483584 = 7704^2 + 3672^2 .

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (72835207) by changing a digit.

It is a polite number, since it can be written in 29 ways as a sum of consecutive naturals, for example, 259060 + ... + 259340.

Almost surely, 2^72835200 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 72835200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (134867205).

72835200 is an abundant number, since it is smaller than the sum of its proper divisors (196899210).

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

72835200 is a wasteful number, since it uses less digits than its factorization.

72835200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 317 (or 291 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The square root of 72835200 is about 8534.3541056134. The cubic root of 72835200 is about 417.6191826305.

The spelling of 72835200 in words is "seventy-two million, eight hundred thirty-five thousand, two hundred".