72349200 has 600 divisors, whose sum is σ = 334889280. Its totient is φ = 14515200.

The previous prime is 72349183. The next prime is 72349201. The reversal of 72349200 is 294327.

It is a tau number, because it is divible by the number of its divisors (600).

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 (72349201) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 2494786 + ... + 2494814.

Almost surely, 2^72349200 is an apocalyptic number.

72349200 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 72349200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (167444640).

72349200 is an abundant number, since it is smaller than the sum of its proper divisors (262540080).

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

72349200 is a wasteful number, since it uses less digits than its factorization.

72349200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 77 (or 57 counting only the distinct ones).

The product of its (nonzero) digits is 3024, while the sum is 27.

The square root of 72349200 is about 8505.8332925117. The cubic root of 72349200 is about 416.6882406607.

The spelling of 72349200 in words is "seventy-two million, three hundred forty-nine thousand, two hundred".