72945600 has 336 divisors, whose sum is σ = 296314368. Its totient is φ = 15298560.

The previous prime is 72945599. The next prime is 72945619. The reversal of 72945600 is 654927.

It is a tau number, because it is divible by the number of its divisors (336).

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 47 ways as a sum of consecutive naturals, for example, 436717 + ... + 436883.

It is an arithmetic number, because the mean of its divisors is an integer number (881888).

Almost surely, 2^72945600 is an apocalyptic number.

72945600 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 72945600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (148157184).

72945600 is an abundant number, since it is smaller than the sum of its proper divisors (223368768).

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

72945600 is a wasteful number, since it uses less digits than its factorization.

72945600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 212 (or 197 counting only the distinct ones).

The product of its (nonzero) digits is 15120, while the sum is 33.

The square root of 72945600 is about 8540.8196327987. The cubic root of 72945600 is about 417.8300782905.

The spelling of 72945600 in words is "seventy-two million, nine hundred forty-five thousand, six hundred".