72085200 has 240 divisors, whose sum is σ = 259792896. Its totient is φ = 16934400.

The previous prime is 72085193. The next prime is 72085207. The reversal of 72085200 is 258027.

It is an interprime number because it is at equal distance from previous prime (72085193) and next prime (72085207).

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

It is a super-3 number, since 3×72085200³ (a number of 25 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72085207) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 567537 + ... + 567663.

Almost surely, 2^72085200 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 72085200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (129896448).

72085200 is an abundant number, since it is smaller than the sum of its proper divisors (187707696).

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

72085200 is a wasteful number, since it uses less digits than its factorization.

72085200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 202 (or 191 counting only the distinct ones).

The product of its (nonzero) digits is 1120, while the sum is 24.

The square root of 72085200 is about 8490.3003480442. The cubic root of 72085200 is about 416.1807954279.

The spelling of 72085200 in words is "seventy-two million, eighty-five thousand, two hundred".