72766800 has 360 divisors, whose sum is σ = 283341240. Its totient is φ = 17203200.

The previous prime is 72766769. The next prime is 72766801. The reversal of 72766800 is 866727.

It can be written as a sum of positive squares in 12 ways, for example, as 27123264 + 45643536 = 5208^2 + 6756^2 .

It is a tau number, because it is divible by the number of its divisors (360).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (72766801) by changing a digit.

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 71 ways as a sum of consecutive naturals, for example, 1774780 + ... + 1774820.

It is an arithmetic number, because the mean of its divisors is an integer number (787059).

Almost surely, 2^72766800 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 72766800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (141670620).

72766800 is an abundant number, since it is smaller than the sum of its proper divisors (210574440).

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

72766800 is a wasteful number, since it uses less digits than its factorization.

72766800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 111 (or 97 counting only the distinct ones).

The product of its (nonzero) digits is 28224, while the sum is 36.

The square root of 72766800 is about 8530.3458312075. The cubic root of 72766800 is about 417.4884120751.

Adding to 72766800 its product of nonzero digits (28224), we get a square (72795024 = 8532²).

The spelling of 72766800 in words is "seventy-two million, seven hundred sixty-six thousand, eight hundred".