72352800 has 216 divisors, whose sum is σ = 275115204. Its totient is φ = 17786880.

The previous prime is 72352793. The next prime is 72352807. The reversal of 72352800 is 825327.

It is an interprime number because it is at equal distance from previous prime (72352793) and next prime (72352807).

It can be written as a sum of positive squares in 6 ways, for example, as 2396304 + 69956496 = 1548^2 + 8364^2 .

It is not an unprimeable number, because it can be changed into a prime (72352807) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 93214 + ... + 93986.

Almost surely, 2^72352800 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 72352800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (137557602).

72352800 is an abundant number, since it is smaller than the sum of its proper divisors (202762404).

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

72352800 is a wasteful number, since it uses less digits than its factorization.

72352800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 812 (or 796 counting only the distinct ones).

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

The square root of 72352800 is about 8506.0449093571. The cubic root of 72352800 is about 416.6951518304.

It can be divided in two parts, 72 and 352800, that multiplied together give a square (25401600 = 5040²).

The spelling of 72352800 in words is "seventy-two million, three hundred fifty-two thousand, eight hundred".